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ﺻﻠﺏ ﺍﻟﺟﺯﻳﺭﺓ ﻟﻠﺧﺭﺳﺎﻧﺔ Sulb Aljazeera Concrete

DESIGN DATA SHEET FOR BOX CULVERT, SAPAC

–ﺍﻟﻤﻤﻠﻜﺔ ﺍﻟﻌﺮﺑﻴﺔﺍﻟﺴﻌﻮﺩﻳﺔ+966 (013) 895 4529 :– ﺗﻠﻔﺎﻛﺲ31473 ﺍﻟﺪﻣﺎﻡ12172 ﺏ.ﻁﺮﻳﻖ ﺑﻘﻴﻖ – ﺹ1080 ﺍﻟﺪﻣﺎﻡ –ﻣﺨﻄﻂ 2nd Industrial Area, Abqaiq Road, Dammam – PO Box 12172 Dammam 31473 – Tel/Fax: +966 (0) 3 895 4529

C.R: 2050092468

www.sulbaljazeera.com

2050092468: ﺕ.ﺱ

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1000 X 800

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

Introduction:

g p (H) above the culvert are as per the Inside dimensions of the box culvert (SPAN x RISE) The fill height below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span p L

1000

Mpa mm

Rise R

800

mm

Top Slab Thickness, Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

4500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec

27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, Es

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1000 X W =800 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 26.40

kN (for 1 m wide)

The self-weight of one culvert side wall is: 4.90

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

34.68

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.64

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

The design vertical earth pressure at the top of the culvert is: 133.07

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

103.32

kN/m

(Bottom)

=

51.66

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressur

0.2827

g for the live load surcharge g calculation at the top p of the culvert is the distance from The height the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5740 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.12 ft 0.65

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.29 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 7.85

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

6.54

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load may not be t taken less th than zero. Th d i l d allowance ll t b k l

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. T d To determine t i th the li live l load, d use multiple lti l presence f factors t (MPF) (MPF). A single i l loaded l d d l lane with ith a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

Axlespacing = Wtire = W =

Ltire =

130 kN

1.8 m 0.51 m 7.49

m

0.25 m

L=

7.23

m

=

5.77

kN/m

Therefore WLL+IM

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing = WLL+IM

=

1.3 m 10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM =

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer: F.

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

17.73 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 275.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400.00

13.63 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 211.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Top Slab

Max @ Mid Slab @IS Max @ Slab End @OS Max @ Slab End @OS

From staad Model Inside

Mu =

27.28 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 427.35

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

427.35

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

4.09 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

k d = thi thickness - C Cover - dm/2 d= As =

155 mm 63.01

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6 67 6.67

DJ

Checked :

Pcs

523 60 523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

20.85 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 256.97

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

14.01 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

k d = thi thickness - C Cover - dm/2 d= As =

195 mm 172.13

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6 67 6.67

DJ

Checked :

Pcs

523 60 523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

107.23 kN

0.17∗√ 60.9 160.92

^′ kN

> Vu u

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

113.58 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

65.09 kN

0.17∗√ 160.92

^′ kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1000 x 800 Top Slab Thickness =

mm

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Dia (mm)

C/C

Dia (mm)

C/C

Top Slab

10

150

10

150

B tt Bottom Sl Slab b

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table A typical section of the culvert is shown in Figure table. Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1000

Mpa mm

Rise R

1000

mm

T Top Slab Sl b Thi Thickness, k Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

4500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 26.40

kN (for 1 m wide)

The self-weight of one culvert side wall is: 5.86

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

36.28

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.64

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 133.07

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

106.92

kN/m

(Bottom)

=

53.46

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5940 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.05 ft 0.63

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.18 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.18

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

36.28

EV =

133.07

kN/m

EHTmax =

81.00

kN/m

EHBmax =

106.92

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

53.46

kN/m

=

3.91

kN/m

LLSbottom =

3.18

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.18

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

17.196 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 267.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400 00 400.00

13.237 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 205.25

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Mid Slab @IS

Max @ Slab End @OS From staad Model Inside

Mu =

27.496 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 430.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

430.81

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

6.618 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 102.13

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

20.383 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 251.16

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

Outside

Mu =

480.00

mm2

mm2

13.623 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 167.35

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

105.468 kN

0.17∗√ 160.92

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

111.385 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

74.07 kN

0.17∗√

^′

160.92

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1000 x 1000 mm Top Slab Thickness =

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 10

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 3000 X 1500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below t bl table. A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

3000

Mpa mm

Rise R

1500

mm

Top Slab Thickness, Tt

320

mm

Thickness Tb Bottom Slab Thickness,

360

mm

4500

mm

Height of Fill H Wall Thickness, Ts

320

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved:

VR

Element BOX CULVERT SAPAC L =3000 X W =1500 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 57.60

kN (for 1 m wide)

The self-weight of one culvert side wall is: 14.13

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

66.23

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.25

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 101.03

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

120.24

kN/m

(Bottom)

=

60.12

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6680 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 14.72

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

13.30

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6 73 6.73

m

where Axlespacing = WLL+IM

1.3 m

=

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

66.23

EV =

101.03

kN/m

EHTmax =

81.00

kN/m

EHBmax =

120.24

kN/m

EHTmin =

40.50

kN/m

EHBmin =

60.12

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

14.72

WAbottomreaction=

13.30

kN/m

LL+IMW =

10.01

kN/m

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

118.29 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,064.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

1,064.84 1 064 84

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Inside

Mu =

640.00

mm2

mm2

64.1 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41

mm2

16

mm

1,340.41

mm2

d = thickness - Cover - dm/2 d= As =

272 mm 569.51

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 640.00

=

640 00 640.00

mm2

mm2

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

139.01 kNm

Main bar dia =

16

mm

1,340.41

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

272 mm 1,257.83

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1,257.83

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

640.00

mm2

mm2

68.21 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

273 mm 604.32 604 32

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 640.00

=

640.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

95.74 kNm

Main bar dia =

16

mm

1,340.41

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

312 mm 743.09

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

743.09

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

720.00

mm2

mm2

110.02 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

313 mm 853.31 853 31

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 853.31

=

720.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

262.78 kN

0.17∗√

^′

281.61

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

228.11 kN

0.17∗√

^′

321.83

kN

> Vu

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

155.38 kN

0.17∗√

(Vc) =

^′

281.61

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 3000 x 1500 mm Top Slab Thickness =

320 mm

Bottom Slab Thickness =

360 mm

Side = id Wall ll Thickness hi k

320 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 14

C/C 150

Bottom Slab

16

150

14

150

Side Wall

16

150

16

150

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2500 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below t bl table. A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2500

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

280

mm

Thickness Tb Bottom Slab Thickness,

320

mm

4500

mm

Height of Fill H Wall Thickness, Ts

280

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2500 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 47.04

kN (for 1 m wide)

The self-weight of one culvert side wall is: 8.74

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

53.44

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.29

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 104.82

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

109.80

kN/m

(Bottom)

=

54.90

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6100 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.82

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6 73 6.73

m

where Axlespacing = WLL+IM

1.3 m

=

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

53.44

EV =

104.82

kN/m

EHTmax =

81.00

kN/m

EHBmax =

109.80

kN/m

EHTmin =

40.50

kN/m

EHBmin =

54.90

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.82

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

86.88 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 913.02

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

913.02 913 02

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided = Inside

560.00

53.33 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

233 mm 554.26

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 560.00

=

560 00 560.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

98.83 kNm

Main bar dia =

16

mm

1,340.41

mm2

12

mm

d = thickness - Cover - dm/2 d= As =

232 mm 1,047.62

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1,047.62

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

47.09 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

234 mm 486.27 486 27

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 560.00

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

73.58 kNm

Main bar dia =

16

mm

1,340.41

mm2

12

mm

d = thickness - Cover - dm/2 d= As =

272 mm 655.21

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

655.21

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

640.00

82 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

274 mm 726.11 726 11

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 726.11

=

640.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

225.17 kN

0.17∗√

^′

241.38

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

207.29 kN

0.17∗√

^′

281.61

kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

121.96 kN

0.17∗√

(Vc) =

^′

241.38

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2500 x 1000 mm Top Slab Thickness =

280 mm

Bottom Slab Thickness =

320 mm

Side = id Wall ll Thickness hi k

280 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

16

150

12

150

Side Wall

14

150

14

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 3000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. yp section of the culvert is shown in Figure. g Material and design g p parameters are g given in Table. A typical

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

3000

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

320

mm

Bottom Slab Thickness, Tb

360

mm

4500

mm

320

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec

27789.4

Mpa

Modulus Elasticity of Steel Reinforcement, Es

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =3000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 57.60

kN (for 1 m wide)

The self-weight of one culvert side wall is: 10.29

kN (for 1 m wide)

Self weight of Haunch 0.03 kN ( (for 1 m wide) )

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B B.

=

63.92

kN (for 1 m wide)

E th P Earth Pressure L Loads d The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.25

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 101.03

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

111 24 111.24

kN/m

(B tt ) (Bottom)

=

55.62

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent q fill height, g , heq q is dependent p on the depth p of fill and can be found using g AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6180 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.03 ft 0.62

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.15 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.86

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7 49 7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

63.92

EV =

101.03

kN/m

EHTmax =

81.00

kN/m

EHBmax =

111.24

kN/m

EHTmin =

40.50

kN/m

EHBmin =

55.62

kN/m

bottom reaction

LLStop

=

3 91 3.91

kN/m

LLSbottom =

3.15

kN/m

WAtop=

F.

kN/m

0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.86

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Ma im m Vertical Load and Ma Maximum im m Hori Horizontal ontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

123.24 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,110.76

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

1,110.76

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided = Inside

640.00

80.63 kNm

150 c/c / 6.67

Pcs

Main bar dia =

1,340.41 16

mm2 mm

d = thickness - Cover - dm/2 d= As =

272 mm 719.20

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 719.20

=

640.00

mm2

mm2

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,340.41

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

133.81 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,209.20

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1 209 20 1,209.20

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

640.00

70.7 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

273 mm 626.75

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 640.00

=

640.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

97.86 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

312 mm 759.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

759 84 759.84

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

720.00

mm2

mm2

111.99 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

313 mm 868.90

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 868.90

=

720.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

264.84 kN

0.17∗√

^′

281.61

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

234.51 kN

0.17∗√

^′

321.83

kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

142.17 kN

0.17∗√

^′

281.61

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 3000 x 1000 mm Top Slab Thickness =

320 mm

Bottom Slab Thickness =

360 mm

Side Wall Thickness =

320 mm

R i f Reinforcement t Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 14

C/C 150

Bottom Slab

16

150

14

150

Side Wall

16

150

16

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2200 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2200

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

4500

mm

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2200 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 38.59

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

44.66

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.34

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 108.20

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

108.36

kN/m

(Bottom)

=

54.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.85

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

44.66

EV =

108.20

kN/m

EHTmax =

81.00

kN/m

EHBmax =

108.36

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

54.18

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.85

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

67.42 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 858.66

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

858.66

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided = Inside

480 00 480.00

60.77 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

193 mm 771.43

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 771.43

=

480.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

74.24 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 948.74

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

948.74

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

35.43 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 441.93

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

59.52 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 619.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

619.84

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

67.49 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 701.54

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 701.54

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

191.69 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

191.55 kN

0.17∗√ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

110.83 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2200 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side Wall Thickness =

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 14

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

14

150

12

150

Side Wall

14

150

14

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2000

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

4500

mm

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Modulus Elasticity of Concrete, Ec

27789.4

Mpa

Modulus d l Elasticity l off Steell Reinforcement, f Es

200000

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium q so external reactions to loads applied pp to the structure were assumed to act equal q and opposite. pp A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 37.44

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

44.04

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.36

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 110.40

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, , a maximum stage g full soil unit weight g and a minimum stage g half soil unit weight g will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

108.36

kN/m

(Bottom)

=

54.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0 61 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.76

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1 20 is used for strength and service limit states 1.20 states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0 51 m 0.51

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

44.04

EV =

110.40

kN/m

EHTmax =

81.00

kN/m

EHBmax =

108.36

kN/m

bottom reaction

EHTmin = T i

40.50 40 50

kN/m

EHBmin =

54.18

kN/m

=

3.91

kN/m

LLSbottom =

3.10

kN/m

LLStop

WAtop=

F.

kN/m

0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.76

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal p distributed reactions applied pp to the bottom slab. Box culverts supported pp on stiff or rigid g subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x ( (d - .0141 * As/2) / )

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

56.943 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

194 mm 717.57

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

717.57

=

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

Inside

Mu =

480.00

mm2

mm2

50.254 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 631.25

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 631.25

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

69.1 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 880.79

mm2

Minimum sidewall flexural reinforcement A i Asmin therefore

= 0.002 0 002 x b x Tt

As =

880.79

=

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

Outside

Mu =

480 00 480.00

mm2 2

mm2

28.65 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 356.23

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

52.204 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 542.36

mm2

Minimum sidewall flexural reinforcement A i Asmin therefore

= 0.002 0 002 x b x Tb

As =

560.00

=

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

Outside

Mu =

560 00 560.00

mm2 2

mm2

55.824 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 578.08

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 578.08

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

185.94 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

178.7 kN

0.17∗√ 0 17 √ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

103.526 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2000 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side Wall Thickness =

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 14

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

14

150

12

150

Side Wall

12

150

12

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1800 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. t bl A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1800

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

3500

mm

Height of Fill H Wall Thickness, Ts

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1800 X W =1000 mm & Depth from GL =3500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 30.53

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

37.76

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1 31 1.31

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

The design vertical earth pressure at the top of the culvert is: 82.34

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 63.00

kN/m

(Top)

31.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

90.36

kN/m

(Bottom)

=

45.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

3500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

heq

Designed:

3500

mm is:

2.85 ft 0.87

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 4.42

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.35 ft 0.72

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.65 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.66

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -14.355 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

6.34

m

0.25 m 6.08

m

8.11

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 5 58 5.58

m

where Axlespacing = WLL+IM

1.3 m

=

14.27

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 14.27 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

37.76

EV =

82.34

kN/m

EHTmax =

63.00

kN/m

EHBmax =

90.36

kN/m

EHTmin =

31.50

kN/m

EHBmin =

45.18

kN/m

=

4.42

kN/m

LLSbottom =

3.65

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.66

kN/m

LL+IMW =

14.27

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

37.9 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 470.77

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

480.00 480 00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

480.00

19.55 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 240.80

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 480.00

=

480 00 480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

48.63 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

194 mm 610.37

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

610.37

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

17.13 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 210.76 210 76

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

32.55 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

234 mm 334.57

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

560.00

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

32.45 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 333.53 333 53

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 560.00

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

139.15 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

170.25 kN

0.17∗√ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

79.95 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1800 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side = id Wall ll Thickness hi k

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 12

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

12

150

12

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1400 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1400

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

220

mm

Bottom Slab Thickness, Tb

260

mm

4500

mm

220

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

ID

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1400 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 31.15

kN (for 1 m wide)

The self-weight of one culvert side wall is: 6.55

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

39.35

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.49

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 120.62

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

107.64

kN/m

(Bottom)

=

53.82

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5980 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.04 ft 0.62

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.16 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.48

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

39.35

EV =

120.62

kN/m

EHTmax =

81.00

kN/m

EHBmax =

107.64

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

53.82

kN/m

=

3.91

kN/m

LLSbottom =

3.16

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.48

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

34.061 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

175 mm 472.41

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

472.41

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

440 00 440.00

28.536 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

175 mm 394.52

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 440.00

=

440.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

46.33 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

174 mm 651.14

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

651.14

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

440.00

13.67 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

175 mm 187.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 440.00

=

440.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

34.81 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

214 mm 392.37

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

520.00

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

520.00

32.12 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

215 mm 359.95

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 520.00

=

520.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

146.68 kN

0.17∗√

^′

181.03

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

146 kN

0.17∗√ 221.26

^′ kN

> Vu

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

87.2 kN

0.17∗√

^′

181.03

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1400 x 1000 mm Top Slab Thickness =

220 mm

Bottom Slab Thickness =

260 mm

Side Wall Thickness =

220 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 12

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

12

150

10

150

Side Wall

10

150

10

150

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1200 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1200

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

3500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1200 X W =1000 mm & Depth from GL =3500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 22.56

kN (for 1 m wide)

The self-weight of one culvert side wall is: 5.86

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

31.05

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.44

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

The design vertical earth pressure at the top of the culvert is: 90.56

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 63.00

kN/m

(Top)

31.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

88.92

kN/m

(Bottom)

=

44.46

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

3500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

heq

Designed:

3500

mm is:

2.7 ft 0.82

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 4.19

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 4940 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.38 ft 0.73

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.69 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.41

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -14.355

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

6.34

m

0.25 m 6.08

m

8.11

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 5.58

m

where Axlespacing =

1.3 m

=

WLL+IM

14.27

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 14 27 kN 14.27 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

31.05

EV =

90.56

kN/m

EHTmax =

63.00

kN/m

EHBmax =

88.92

kN/m

EHTmin =

31.50

kN/m

EHBmin =

bottom reaction

44.46

kN/m

=

4.19

kN/m

LLSbottom =

3.69

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.41

kN/m

LL+IMW =

14 27 14.27

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

18 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 280.07

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400 00 400.00

14.75 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 228.96

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Top Slab

Max @ Mid Slab @IS

Max @ Slab End @OS From staad Model Inside

Mu =

26.62 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 416.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

416.81

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

6.57 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 101.39

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

17.95 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 220.93

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

14.77 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 181.53

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

97.78 kN

0.17∗√ 160.92

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

89.16 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

63.79 kN

0.17∗√

^′

160.92

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1200 x 1000 mm Top Slab Thickness =

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 10

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

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DESIGN DATA SHEET FOR BOX CULVERT, SAPAC

–ﺍﻟﻤﻤﻠﻜﺔ ﺍﻟﻌﺮﺑﻴﺔﺍﻟﺴﻌﻮﺩﻳﺔ+966 (013) 895 4529 :– ﺗﻠﻔﺎﻛﺲ31473 ﺍﻟﺪﻣﺎﻡ12172 ﺏ.ﻁﺮﻳﻖ ﺑﻘﻴﻖ – ﺹ1080 ﺍﻟﺪﻣﺎﻡ –ﻣﺨﻄﻂ 2nd Industrial Area, Abqaiq Road, Dammam – PO Box 12172 Dammam 31473 – Tel/Fax: +966 (0) 3 895 4529

C.R: 2050092468

www.sulbaljazeera.com

2050092468: ﺕ.ﺱ

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1000 X 800

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

Introduction:

g p (H) above the culvert are as per the Inside dimensions of the box culvert (SPAN x RISE) The fill height below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span p L

1000

Mpa mm

Rise R

800

mm

Top Slab Thickness, Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

4500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec

27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, Es

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1000 X W =800 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 26.40

kN (for 1 m wide)

The self-weight of one culvert side wall is: 4.90

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

34.68

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.64

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

The design vertical earth pressure at the top of the culvert is: 133.07

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

103.32

kN/m

(Bottom)

=

51.66

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressur

0.2827

g for the live load surcharge g calculation at the top p of the culvert is the distance from The height the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5740 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.12 ft 0.65

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.29 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 7.85

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

6.54

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load may not be t taken less th than zero. Th d i l d allowance ll t b k l

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. T d To determine t i th the li live l load, d use multiple lti l presence f factors t (MPF) (MPF). A single i l loaded l d d l lane with ith a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

Axlespacing = Wtire = W =

Ltire =

130 kN

1.8 m 0.51 m 7.49

m

0.25 m

L=

7.23

m

=

5.77

kN/m

Therefore WLL+IM

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing = WLL+IM

=

1.3 m 10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM =

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer: F.

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

17.73 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 275.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400.00

13.63 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 211.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Top Slab

Max @ Mid Slab @IS Max @ Slab End @OS Max @ Slab End @OS

From staad Model Inside

Mu =

27.28 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 427.35

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

427.35

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

4.09 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

k d = thi thickness - C Cover - dm/2 d= As =

155 mm 63.01

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6 67 6.67

DJ

Checked :

Pcs

523 60 523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

20.85 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 256.97

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

14.01 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

k d = thi thickness - C Cover - dm/2 d= As =

195 mm 172.13

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6 67 6.67

DJ

Checked :

Pcs

523 60 523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

107.23 kN

0.17∗√ 60.9 160.92

^′ kN

> Vu u

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

113.58 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

65.09 kN

0.17∗√ 160.92

^′ kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1000 x 800 Top Slab Thickness =

mm

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Dia (mm)

C/C

Dia (mm)

C/C

Top Slab

10

150

10

150

B tt Bottom Sl Slab b

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =800 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table A typical section of the culvert is shown in Figure table. Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1000

Mpa mm

Rise R

1000

mm

T Top Slab Sl b Thi Thickness, k Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

4500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 26.40

kN (for 1 m wide)

The self-weight of one culvert side wall is: 5.86

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

36.28

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.64

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 133.07

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

106.92

kN/m

(Bottom)

=

53.46

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5940 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.05 ft 0.63

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.18 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.18

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

36.28

EV =

133.07

kN/m

EHTmax =

81.00

kN/m

EHBmax =

106.92

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

53.46

kN/m

=

3.91

kN/m

LLSbottom =

3.18

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.18

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

17.196 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 267.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400 00 400.00

13.237 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 205.25

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Mid Slab @IS

Max @ Slab End @OS From staad Model Inside

Mu =

27.496 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 430.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

430.81

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

6.618 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 102.13

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

20.383 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 251.16

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

Outside

Mu =

480.00

mm2

mm2

13.623 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 167.35

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

105.468 kN

0.17∗√ 160.92

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

111.385 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

74.07 kN

0.17∗√

^′

160.92

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1000 x 1000 mm Top Slab Thickness =

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 10

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 3000 X 1500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below t bl table. A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

3000

Mpa mm

Rise R

1500

mm

Top Slab Thickness, Tt

320

mm

Thickness Tb Bottom Slab Thickness,

360

mm

4500

mm

Height of Fill H Wall Thickness, Ts

320

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved:

VR

Element BOX CULVERT SAPAC L =3000 X W =1500 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 57.60

kN (for 1 m wide)

The self-weight of one culvert side wall is: 14.13

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

66.23

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.25

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 101.03

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

120.24

kN/m

(Bottom)

=

60.12

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6680 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 14.72

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

13.30

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6 73 6.73

m

where Axlespacing = WLL+IM

1.3 m

=

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

66.23

EV =

101.03

kN/m

EHTmax =

81.00

kN/m

EHBmax =

120.24

kN/m

EHTmin =

40.50

kN/m

EHBmin =

60.12

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

14.72

WAbottomreaction=

13.30

kN/m

LL+IMW =

10.01

kN/m

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

118.29 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,064.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

1,064.84 1 064 84

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Inside

Mu =

640.00

mm2

mm2

64.1 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41

mm2

16

mm

1,340.41

mm2

d = thickness - Cover - dm/2 d= As =

272 mm 569.51

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 640.00

=

640 00 640.00

mm2

mm2

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

139.01 kNm

Main bar dia =

16

mm

1,340.41

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

272 mm 1,257.83

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1,257.83

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

640.00

mm2

mm2

68.21 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

273 mm 604.32 604 32

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 640.00

=

640.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

95.74 kNm

Main bar dia =

16

mm

1,340.41

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

312 mm 743.09

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

743.09

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

720.00

mm2

mm2

110.02 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

313 mm 853.31 853 31

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 853.31

=

720.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

262.78 kN

0.17∗√

^′

281.61

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

228.11 kN

0.17∗√

^′

321.83

kN

> Vu

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

155.38 kN

0.17∗√

(Vc) =

^′

281.61

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 3000 x 1500 mm Top Slab Thickness =

320 mm

Bottom Slab Thickness =

360 mm

Side = id Wall ll Thickness hi k

320 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 14

C/C 150

Bottom Slab

16

150

14

150

Side Wall

16

150

16

150

Designed:

DJ

Checked :

VR

Approved:

VR

L =3000 X W =1500 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2500 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below t bl table. A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2500

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

280

mm

Thickness Tb Bottom Slab Thickness,

320

mm

4500

mm

Height of Fill H Wall Thickness, Ts

280

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2500 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 47.04

kN (for 1 m wide)

The self-weight of one culvert side wall is: 8.74

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

53.44

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.29

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 104.82

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

109.80

kN/m

(Bottom)

=

54.90

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6100 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.82

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6 73 6.73

m

where Axlespacing = WLL+IM

1.3 m

=

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

53.44

EV =

104.82

kN/m

EHTmax =

81.00

kN/m

EHBmax =

109.80

kN/m

EHTmin =

40.50

kN/m

EHBmin =

54.90

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.82

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

86.88 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 913.02

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

913.02 913 02

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided = Inside

560.00

53.33 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25

mm2

14

mm

1,026.25

mm2

d = thickness - Cover - dm/2 d= As =

233 mm 554.26

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 560.00

=

560 00 560.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

98.83 kNm

Main bar dia =

16

mm

1,340.41

mm2

12

mm

d = thickness - Cover - dm/2 d= As =

232 mm 1,047.62

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1,047.62

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

47.09 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

234 mm 486.27 486 27

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 560.00

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

73.58 kNm

Main bar dia =

16

mm

1,340.41

mm2

12

mm

d = thickness - Cover - dm/2 d= As =

272 mm 655.21

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

655.21

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

640.00

82 kNm

150 c/c 6.67

Pcs

Main bar dia =

d = thickness - Cover - dm/2 d= As =

274 mm 726.11 726 11

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 726.11

=

640.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

225.17 kN

0.17∗√

^′

241.38

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

207.29 kN

0.17∗√

^′

281.61

kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

121.96 kN

0.17∗√

(Vc) =

^′

241.38

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2500 x 1000 mm Top Slab Thickness =

280 mm

Bottom Slab Thickness =

320 mm

Side = id Wall ll Thickness hi k

280 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

16

150

12

150

Side Wall

14

150

14

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2500 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 3000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. yp section of the culvert is shown in Figure. g Material and design g p parameters are g given in Table. A typical

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

3000

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

320

mm

Bottom Slab Thickness, Tb

360

mm

4500

mm

320

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec

27789.4

Mpa

Modulus Elasticity of Steel Reinforcement, Es

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =3000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 57.60

kN (for 1 m wide)

The self-weight of one culvert side wall is: 10.29

kN (for 1 m wide)

Self weight of Haunch 0.03 kN ( (for 1 m wide) )

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B B.

=

63.92

kN (for 1 m wide)

E th P Earth Pressure L Loads d The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.25

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 101.03

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

111 24 111.24

kN/m

(B tt ) (Bottom)

=

55.62

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka =

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent q fill height, g , heq q is dependent p on the depth p of fill and can be found using g AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6180 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.03 ft 0.62

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.15 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.86

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

configuration produces a live load intensity of:

7 49 7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

63.92

EV =

101.03

kN/m

EHTmax =

81.00

kN/m

EHBmax =

111.24

kN/m

EHTmin =

40.50

kN/m

EHBmin =

55.62

kN/m

bottom reaction

LLStop

=

3 91 3.91

kN/m

LLSbottom =

3.15

kN/m

WAtop=

F.

kN/m

0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.86

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Ma im m Vertical Load and Ma Maximum im m Hori Horizontal ontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

123.24 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,110.76

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

1,110.76

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided = Inside

640.00

80.63 kNm

150 c/c / 6.67

Pcs

Main bar dia =

1,340.41 16

mm2 mm

d = thickness - Cover - dm/2 d= As =

272 mm 719.20

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 719.20

=

640.00

mm2

mm2

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,340.41

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

133.81 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

272 mm 1,209.20

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

1 209 20 1,209.20

=

16 mm dia X

for 1 m length

16 mm dia X Mu =

mm2

mm2

As Provided =

Outside

640.00

70.7 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

273 mm 626.75

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 640.00

=

640.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

97.86 kNm

Main bar dia =

16

mm

d = thickness - Cover - dm/2 d= As =

312 mm 759.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

759 84 759.84

=

As Provided =

16 mm dia X

for 1 m length

16 mm dia X

Outside

Mu =

720.00

mm2

mm2

111.99 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,340.41 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

313 mm 868.90

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 868.90

=

720.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

264.84 kN

0.17∗√

^′

281.61

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

234.51 kN

0.17∗√

^′

321.83

kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

142.17 kN

0.17∗√

^′

281.61

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 3000 x 1000 mm Top Slab Thickness =

320 mm

Bottom Slab Thickness =

360 mm

Side Wall Thickness =

320 mm

R i f Reinforcement t Inside

Location

Outside

Top Slab

Dia (mm) 16

C/C 150

Dia (mm) 14

C/C 150

Bottom Slab

16

150

14

150

Side Wall

16

150

16

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =3000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2200 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2200

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

4500

mm

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2200 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 38.59

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

44.66

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.34

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 108.20

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

108.36

kN/m

(Bottom)

=

54.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.85

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

44.66

EV =

108.20

kN/m

EHTmax =

81.00

kN/m

EHBmax =

108.36

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

54.18

kN/m

=

3.91

kN/m

LLSbottom =

3.10

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.85

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

67.42 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 858.66

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

858.66

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided = Inside

480 00 480.00

60.77 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 14

mm2 mm

d = thickness - Cover - dm/2 d= As =

193 mm 771.43

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 771.43

=

480.00

mm2

mm2

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

1,026.25

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

74.24 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 948.74

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

948.74

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

35.43 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 441.93

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

59.52 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 619.84

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

619.84

=

14 mm dia X

for 1 m length

14 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

67.49 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 701.54

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 701.54

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

191.69 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

191.55 kN

0.17∗√ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

110.83 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2200 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side Wall Thickness =

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 14

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

14

150

12

150

Side Wall

14

150

14

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2200 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 2000 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

2000

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

4500

mm

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

420

Mpa

Modulus Elasticity of Concrete, Ec

27789.4

Mpa

Modulus d l Elasticity l off Steell Reinforcement, f Es

200000

Mpa

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =2000 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium q so external reactions to loads applied pp to the structure were assumed to act equal q and opposite. pp A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 37.44

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

44.04

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.36

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 110.40

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, , a maximum stage g full soil unit weight g and a minimum stage g half soil unit weight g will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

108.36

kN/m

(Bottom)

=

54.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 6020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2 ft 0 61 0.61

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.10 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.76

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1 20 is used for strength and service limit states 1.20 states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0 51 m 0.51

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10.01 kN therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

44.04

EV =

110.40

kN/m

EHTmax =

81.00

kN/m

EHBmax =

108.36

kN/m

bottom reaction

EHTmin = T i

40.50 40 50

kN/m

EHBmin =

54.18

kN/m

=

3.91

kN/m

LLSbottom =

3.10

kN/m

LLStop

WAtop=

F.

kN/m

0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.76

kN/m

LL+IMW =

10.01

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal p distributed reactions applied pp to the bottom slab. Box culverts supported pp on stiff or rigid g subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x ( (d - .0141 * As/2) / )

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

56.943 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

194 mm 717.57

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

717.57

=

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

Inside

Mu =

480.00

mm2

mm2

50.254 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 631.25

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 631.25

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

69.1 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

193 mm 880.79

mm2

Minimum sidewall flexural reinforcement A i Asmin therefore

= 0.002 0 002 x b x Tt

As =

880.79

=

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

Outside

Mu =

480 00 480.00

mm2 2

mm2

28.65 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

194 mm 356.23

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

52.204 kNm

Main bar dia =

14

mm

d = thickness - Cover - dm/2 d= As =

233 mm 542.36

mm2

Minimum sidewall flexural reinforcement A i Asmin therefore

= 0.002 0 002 x b x Tb

As =

560.00

=

As Provided =

14 mm dia X

for 1 m length

14 mm dia X

Outside

Mu =

560 00 560.00

mm2 2

mm2

55.824 kNm

150 c/c 6.67

Pcs

Main bar dia =

1,026.25 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 578.08

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 578.08

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

185.94 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

178.7 kN

0.17∗√ 0 17 √ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

103.526 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 2000 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side Wall Thickness =

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 14

C/C 150

Dia (mm) 12

C/C 150

Bottom Slab

14

150

12

150

Side Wall

12

150

12

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =2000 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1800 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. t bl A t typical i l section ti of f th the culvert l t i is shown h i in Fi Figure. M Material t i l and d d design i parameters t are given i i in T Table. bl

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1800

Mpa mm

Rise R

1000

mm

Top Slab Thickness, Tt

240

mm

Bottom Slab Thickness, Tb

280

mm

3500

mm

Height of Fill H Wall Thickness, Ts

240

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1800 X W =1000 mm & Depth from GL =3500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 30.53

kN (for 1 m wide)

The self-weight of one culvert side wall is: 7.26

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

37.76

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1 31 1.31

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

The design vertical earth pressure at the top of the culvert is: 82.34

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For at-rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 63.00

kN/m

(Top)

31.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

90.36

kN/m

(Bottom)

=

45.18

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top p of culvert

=

3500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

heq

Designed:

3500

mm is:

2.85 ft 0.87

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 4.42

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5020 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.35 ft 0.72

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.65 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.66

kN/m

(Span + Ts) E.

Live Load The design live loads include the HL-93 truck and tandem loads. Since the span of the box culvert is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -14.355 The dynamic load allowance may not be taken less than zero.

=

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength g and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

6.34

m

0.25 m 6.08

m

8.11

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 5 58 5.58

m

where Axlespacing = WLL+IM

1.3 m

=

14.27

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 14.27 kN therefore WLL+IM = Final Loading DC DC

bottom reaction

=

Sel weight of Culvert

=

37.76

EV =

82.34

kN/m

EHTmax =

63.00

kN/m

EHBmax =

90.36

kN/m

EHTmin =

31.50

kN/m

EHBmin =

45.18

kN/m

=

4.42

kN/m

LLSbottom =

3.65

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.66

kN/m

LL+IMW =

14.27

kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin 3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EHmax + 1.00LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied to the culvert (earth, water, live load) are assumed to be carried by uniform, triangular or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner corner. Reinforcement Design

where, F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Side Wall

Max @ Mid Slab@IS Max @ Slab End@OS

From staad Model Outside

Mu =

37.9 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 470.77

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Ts

As =

480.00 480 00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

480.00

19.55 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 240.80

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 0 002 x b x Ts 480.00

=

480 00 480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

48.63 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

194 mm 610.37

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

610.37

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

17.13 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 210.76 210 76

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

32.55 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

234 mm 334.57

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

560.00

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

560.00

32.45 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 12

mm2 mm

d = thickness - Cover - dm/2 d= As =

234 mm 333.53 333 53

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 560.00

=

560.00

mm2

mm2

As Provided =

12 mm dia X

for 1 m length

12 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

753.98

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

139.15 kN

0.17∗√ 201.15

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

170.25 kN

0.17∗√ 241.38

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

79.95 kN

0.17∗√

^′

201.15

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1800 x 1000 mm Top Slab Thickness =

240 mm

Bottom Slab Thickness =

280 mm

Side = id Wall ll Thickness hi k

240 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 12

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

12

150

12

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1800 X W =1000 mm & Depth from GL =3500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1400 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1400

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

220

mm

Bottom Slab Thickness, Tb

260

mm

4500

mm

220

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

ID

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1400 X W =1000 mm & Depth from GL =4500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 31.15

kN (for 1 m wide)

The self-weight of one culvert side wall is: 6.55

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

39.35

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.49

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

The design vertical earth pressure at the top of the culvert is: 120.62

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 81.00

kN/m

(Top)

40.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

107.64

kN/m

(Bottom)

=

53.82

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

4500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

heq

Designed:

4500

mm is:

2.52 ft 0.77

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 3.91

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 5980 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.04 ft 0.62

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.16 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.48

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -27.885

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

7.49

m

0.25 m 7.23

m

5.77

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 6.73

m

where Axlespacing =

1.3 m

=

WLL+IM

10.01

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 10 01 kN 10.01 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

39.35

EV =

120.62

kN/m

EHTmax =

81.00

kN/m

EHBmax =

107.64

kN/m

EHTmin =

40.50

kN/m

EHBmin =

bottom reaction

53.82

kN/m

=

3.91

kN/m

LLSbottom =

3.16

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.48

kN/m

LL+IMW =

10 01 10.01

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

34.061 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

175 mm 472.41

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

472.41

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

440 00 440.00

28.536 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

175 mm 394.52

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 440.00

=

440.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Top Slab

Max @ Slab End @OS

Max @ Mid Slab @IS

From staad Model Inside

Mu =

46.33 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

174 mm 651.14

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

651.14

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

440.00

13.67 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

175 mm 187.40

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 440.00

=

440.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

34.81 kNm

Main bar dia =

12

mm

d = thickness - Cover - dm/2 d= As =

214 mm 392.37

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

520.00

=

12 mm dia X

for 1 m length

12 mm dia X Mu =

mm2

mm2

As Provided =

Outside

520.00

32.12 kNm

150 c/c 6.67

Pcs

Main bar dia =

753.98 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

215 mm 359.95

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 520.00

=

520.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

ID

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

146.68 kN

0.17∗√

^′

181.03

kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

146 kN

0.17∗√ 221.26

^′ kN

> Vu

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

87.2 kN

0.17∗√

^′

181.03

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1400 x 1000 mm Top Slab Thickness =

220 mm

Bottom Slab Thickness =

260 mm

Side Wall Thickness =

220 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 12

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

12

150

10

150

Side Wall

10

150

10

150

Designed:

ID

Checked :

VR

Approved :

VR

L =1400 X W =1000 mm & Depth from GL =4500

SULB AL‐JAZEERA CONCRETE MANUFACTURING Project: Client:

BOX CULVERT

Designed:

DJ

Checked :

VR

Approved :

VR

Location: SAUDI ARABIA

SAPAC

BOX CULVERT SIZE 1200 X 1000

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Introduction:

Inside dimensions of the box culvert (SPAN x RISE) The fill height (H) above the culvert are as per the below table. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table.

Material and Design Parameters Reinforced Concrete, c

24

kN/m3

Soil, s

18

kN/m3

Compressive Strength, f’c

35

Span L

1200

Mpa mm

Rise R

1000

mm

T Top Sl Slab b Thi Thickness, k Tt

200

mm

Bottom Slab Thickness, Tb

240

mm

3500

mm

200

mm

Haunch Thickness, Th

50

mm

Reinforcement Clear Cover

40

mm

Height of Fill H Wall Thickness, Ts

Yield Strength, fy

Modulus Elasticity of Concrete, Ec Modulus Elasticity of Steel Reinforcement, Es

420

Mpa

27789.4

Mpa

200000

Mpa

SULB AL-JAZEERA CONCRETE MANUFACTURING

Designed:

DJ

Checked :

VR

Approved :

VR

Element BOX CULVERT SAPAC L =1200 X W =1000 mm & Depth from GL =3500 Customer: Size: The approximate strip method is used for the design with the 1m wide design strip oriented parallel to the direction of traffic. A 2-Dimensional (2D) plane frame model is used to analyze the box culvert. Beam elements in the 2D model are assumed to be centered in the concrete members. The model is assumed to be externally supported by a pinned support on one end and a roller support on the other end. In addition, the model is always assumed to be in equilibrium so external reactions to loads applied to the structure were assumed to act equal and opposite opposite. A “w” dimension of 1 m is added to the calculations to convert the units to kN/m for consistency with national conventions.

A.

Dead Load The total self-weight of

the culvert top slab is: 22.56

kN (for 1 m wide)

The self-weight of one culvert side wall is: 5.86

kN (for 1 m wide)

Self weight of Haunch 0.03 kN (for 1 m wide)

The top slab weight, wall weights, and all four haunch weights are applied to the bottom slab as an upward reaction from the soil assuming an equivalent uniform pressure. The bottom slab weight is not applied in the model because its load is assumed to be directly resisted by the soil.

Dc bottom B.

=

31.05

kN (for 1 m wide)

Earth Pressure Loads The weight of fill on top of the culvert produces vertical earth pressure (EV). The fill height is measured from the top surface of the top slab to the top of the pavement or fill. The unit weight of the fill is 19.2 kN/m3 The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc): 1.44

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

The design vertical earth pressure at the top of the culvert is: 90.56

kN/m

The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. For atrest conditions conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used. At the top of the culvert, the lateral earth pressure is: 63.00

kN/m

(Top)

31.50

kN/m

(Top)

At the bottom of the culvert, the lateral earth pressure is:

C.

=

88.92

kN/m

(Bottom)

=

44.46

kN/m

(Bottom)

Live Load Surcharge Use an active coefficient of lateral earth pressure ka

0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from the top surface of the top slab to the top of the pavement or fill. The height is: H

top of culvert

=

3500 mm

The equivalent fill height, heq is dependent on the depth of fill and can be found using AASHTO Table 3.11.6.4-1.

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

By interpolation, the equivalent height for a fill depth of =

heq

=

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

heq

Designed:

3500

mm is:

2.7 ft 0.82

m

The corresponding lateral live load surcharge on the top of the culvert is given as: 4.19

kN/m

The height for the live load surcharge calculation at the bottom of the culvert is the distance from the bottom surface of the bottom slab to the top of the pavement or fill. 4940 mm Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq

=

heq

=

2.38 ft 0.73

m

The lateral live load surcharge located at the bottom of the culvert is given as: 3.69 D.

kN/m

Water Load Designers need to consider load cases where the culvert is full of water as well as cases where the culvert is empty. A simple hydrostatic distribution is used for the water load: At the inside of the culvert, the lateral water pressure is: WAtop =

0 kN/m2 9.81

kN/m2

Using a 2D frame model there is an opposite upward reaction from the soil caused by the water inside the culvert: Wabottom

reaction

=

WA bottom * Span

=

8.41

kN/m

(Span + Ts) E.

Live Load The d Th design i li live l loads d i include l d th the HL HL-93 93 t truck k and d t tandem d l loads. d Si Since th the span of f th the b box culvert l t i is less than 15 ft, no lane load is applied. Dynamic Load Allowance The dynamic load allowance (IM) for culverts and other buried structures is reduced based on the depth of fill over the culvert. For strength and service limit states: -14.355

=

The dynamic load allowance may not be taken less than zero.

0

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Live Load Distribution Live loads are assumed to distribute laterally with depth. The specifications permit designers to increase the footprint of the load with increasing depth of fill. The load is assumed to spread laterally 1.15 times H horizontally in each direction for every foot of fill above the culvert. The intensity of live loads at any depth is assumed to be uniform over the entire footprint.

The assumed tire contact area for each wheel has a width of 20 inches and a length of 10 inches.

Using the distances between wheel lines and axles, the live load intensities at the top of the box culvert can be found. For truck and tandem loadings, the influence area or footprint of the live load is found first. Then the sum of the weights of the wheels is used to determine the intensity of the live load. To determine the live load, use multiple presence factors (MPF). A single loaded lane with a MPF of 1.20 is used for strength and service limit states. A single 3 Axle

where

with 600 kN Truck

Pw =

130 kN

Axlespacing =

1.8 m

Wtire =

0.51 m

W =

Ltire = L=

6.34

m

0.25 m 6.08

m

8.11

kN/m

Therefore WLL+IM

=

configuration produces a live load intensity of:

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

A tandem truck axle configuration produces a live load intensity of:

where

Pw =

105 kN 5.58

m

where Axlespacing =

1.3 m

=

WLL+IM

14.27

kN/m

The live load intensities of the single and tandem axle configurations are compared. Since the tandem axle configuration produces a live load intensity slightly larger than that of the single axle configuration, the tandem axle configuration is used for design in both the strength and service limit states. 14 27 kN 14.27 therefore WLL+IM = Final Loading DC DC

=

Sel weight of Culvert

=

31.05

EV =

90.56

kN/m

EHTmax =

63.00

kN/m

EHBmax =

88.92

kN/m

EHTmin =

31.50

kN/m

EHBmin =

bottom reaction

44.46

kN/m

=

4.19

kN/m

LLSbottom =

3.69

LLStop

WAtop=

F.

kN/m

kN/m 0 kN/m

WAbottom=

9.81

kN/m

WAbottomreaction=

8.41

kN/m

LL+IMW =

14 27 14.27

kN/ kN/m

Load Combination Strength Limit states 1 Maximum Vertical Load and Maximum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+ (1.35)(1.05)EHmax + 1.75LS 2 Maximum Vertical Lod and Minimum Horizontal Load 1.25 DC + (1.30)(1.05) EV +1.75 (LL+IM)+1.00WA+(0.9/1.05)EHmin

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

3 Minimum Vertical load and Maximum Horizontal Load 0.90 DC + (0.9/1.05)EV + (1.35)(1.05) EHmax +1.75LS Service Limit State 1 Maximum Vertical Load and Maximum Horizontal Load (LL+IM)+1.00EH 1.00 .00 DC C + 1.00 .00 EV + 1.00 .00 ( ) .00 max + 1.00LS .00 S 2 Maximum Vertical Lod and Minimum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00WA+1.00EHmin 3 Minimum Vertical load and Maximum Horizontal Load 1.00 DC + 1.00EV + 1.00EHmax +1.00LS

A structural analysis is performed using a standard commercial matrix-analysis program. The bottom slab of the box culvert is assumed rigid compared to the subgrade. Reactions to vertical loads applied li d to the h culvert l ( (earth, h water, li live l load) d) are assumed d to b be carried i d b by uniform, if triangular i l or trapezoidal distributed reactions applied to the bottom slab. Box culverts supported on stiff or rigid subgrades (rock) would require further investigation. The haunches are included in the analysis by increasing the thickness of members near each corner. Reinforcement Design

where, where F =

1

fy =

420 Mpa

fc' =

35 MPa

b =

1 m

therefore, a =

As x 420 0.85 x 35 x1000

a=

420∗

0.0141

As

Mu =

1 x As x 420 x (d - .0141 * As/2)

Mu =

420 x As*d - 2.961 As^2

√ 176400 ^2 11.844

/5.922

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Side Wall

Max @ Mid Slab@IS

Max @ Slab End@OS

From staad Model Outside

Mu =

18 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 280.07

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 0 002 x b x Ts

As =

400.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided = Inside

400 00 400.00

14.75 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 228.96

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Ts 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Top Slab

Max @ Mid Slab @IS

Max @ Slab End @OS From staad Model Inside

Mu =

26.62 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

155 mm 416.81

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tt

As =

416.81

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

400.00

6.57 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

155 mm 101.39

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tt 400.00

=

400.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Designed:

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

Size:

Bottom Slab

Max @ Slab End@OS Max @ Mid Slab @IS

From staad Model Inside

Mu =

17.95 kNm

Main bar dia =

10

mm

d = thickness - Cover - dm/2 d= As =

195 mm 220.93

mm2

Minimum sidewall flexural reinforcement Asmin therefore

= 0.002 x b x Tb

As =

480.00

=

10 mm dia X

for 1 m length

10 mm dia X Mu =

mm2

mm2

As Provided =

Outside

480.00

14.77 kNm

150 c/c 6.67

Pcs

Main bar dia =

523.60 10

mm2 mm

d = thickness - Cover - dm/2 d= As =

195 mm 181.53

mm2

Minimum sidewall flexural reinforcement Asmin therefore

As =

= 0.002 x b x Tb 480.00

=

480.00

mm2

mm2

As Provided =

10 mm dia X

for 1 m length

10 mm dia X

150 c/c 6.67

DJ

Checked :

Pcs

523.60

mm2

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Checking of Shear Top Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

97.78 kN

0.17∗√ 160.92

^′ kN

> Vu

Bottom Slab

Maximum Shear (Vu) = Shear Capacity

(Vc) =

89.16 kN

0.17∗√ 201.15

^′ kN

> Vu

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

SULB AL-JAZEERA CONCRETE MANUFACTURING Element BOX CULVERT Customer:

SAPAC

Size:

Side Wall

Maximum Shear (Vu) = Shear Capacity

(Vc) =

63.79 kN

0.17∗√

^′

160.92

kN

> Vu

Final Size and Reinforcement Box culvert Inside Dimensions = 1200 x 1000 mm Top Slab Thickness =

200 mm

Bottom Slab Thickness =

240 mm

Side Wall Thickness =

200 mm

Reinforcement Inside

Location

Outside

Top Slab

Dia (mm) 10

C/C 150

Dia (mm) 10

C/C 150

Bottom Slab

10

150

10

150

Side Wall

10

150

10

150

Designed:

DJ

Checked :

VR

Approved :

VR

L =1200 X W =1000 mm & Depth from GL =3500

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