Design Data Sheet for Box Culvert

(1)

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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

DESIGN DATA

SHEET FOR BOX

CULVERT, SAPAC

(2)

Client:

SAPAC

(3)

Customer: Size: Introduction:

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

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

24 _kN/m3 18 kN/m3 35 Mpa 1000 mm Material and Design Parameters

Reinforced Concrete, c Soil, s Compressive Strength, f’c Span L 800 mm 200 mm 240 mm 4500 mm 200 mm 50 mm 40 mm Wall Thickness, Ts Reinforcement Clear Cover Haunch Thickness, Th

p Rise R

Top Slab Thickness, Tt Bottom Slab Thickness, Tb Height of Fill H

420 Mpa 27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, E

s 200000 Mpa

Yield Strength, fy

(4)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 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.

Dcbottom = 34.68 kN (for 1 m wide)

B. Earth Pressure Loads

the model because its load is assumed to be directly resisted by the soil.

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

1.64 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):

(5)

Customer: SAPAC Size: 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

at-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:

rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used.

= 103.32 kN/m (Bottom)

= 51.66 kN/m (Bottom)

C. Live Load Surcharge

Use an active coefficient of lateral earth pressur 0.2827

The height for the live load surcharge calculation at the top of the culvert is the distance from The height is:

H top of culvert = 4500 mm

g g p

the top surface of the top slab to the top of the pavement or fill.

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

(6)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500

By interpolation, the equivalent height for a fill depth of 4500 mm is: heq = 2.52ft

heq = 0.77 m

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

kN/m

5740 mm

Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is:

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.

heq = 2.12ft

heq = 0.65 m

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

kN/m D. 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

Dynamic Load Allowance

-27.885 = 0 Th d i l d ll t b t k l th

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.

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:

(7)

Customer: SAPAC Size: 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 t i th li l d lti l f t (MPF) A i l l d d l ith MPF

where Pw = 130kN

A single 3 Axle with 600 kN Truck configuration produces a live load intensity of:

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.

Axlespacing = 1.8m Wtire = 0.51m W = 7.49 m Ltire = 0.25m L= 7.23 m Therefore WLL+IM = 5.77 kN/m

(8)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 A tandem truck axle configuration produces a live load intensity of:

where Pw = 105 kN where Pw 105 kN 6.73 m where Axlespacing = 1.3m 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 therefore WLL+IM = 10.01 kN

(9)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 F. 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 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,

Reinforcement Design

where,

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.

F = 1 fy = 420 Mpa fc' = 35 MPa b = 1 m therefore, a = As x 420 0.85 x 35 x1000 a= 0.0141 As Mu = 1 x As x 420 x (d - .0141 * As/2) Mu = 420 x As*d - 2.961 As^2

420∗

√ 176400 ^2 11.844

/5.922

(10)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 Side Wall

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

From staad Model

Outside Mu = 17.73 kNm Main bar dia = 10 mm d = thickness - Cover - dm/2

d= 155 mm As = 275.81 mm2

Minimum sidewall flexural reinforcement

Asmin = 0.002 x b x Ts = mm2400.00 therefore As = 400.00 mm2

As Provided = 10 mm dia X 150 c/c

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2 Inside Mu = 13.63 kNm Main bar dia = 10 mm

d = thickness - Cover - dm/2

d= 155 mm d= 155 mm As = 211.40 mm2

Asmin = 0.002 x b x Ts = mm2400.00 therefore As = 400.00 mm2

(11)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 Top Slab

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

Inside Mu = 27.28 kNm Main bar dia = 10 mm d = thickness - Cover - dm/2

d= 155 mm As = 427.35 mm2

Max @ Slab End @OS

Asmin = 0.002 x b x Tt = mm2400.00 therefore As = 427.35 mm2

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2

Outside Mu = 4.09 kNm Main bar dia = 10 mm d thi k C d /2

d= 155 mm As = 63.01 mm2

Asmin = 0.002 x b x Tt = mm2400.00 therefore As = 400.00 mm2

for 1 m length 10 mm dia X 6 67 Pcs 523 60 mm2 for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2

(12)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 Bottom Slab

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

d= 195 mm As = 256.97 mm2

Asmin = 0.002 x b x Tb = mm2480.00 therefore As = 480.00 mm2

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2

Outside Mu = 14.01 kNm Main bar dia = 10 mm d thi k C d /2

d= 195 mm As = 172.13 mm2

Asmin = 0.002 x b x Tb = mm2480.00 therefore As = 480.00 mm2

for 1 m length 10 mm dia X 6 67 Pcs 523 60 mm2 for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2

(13)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 Checking of Shear

Top Slab

Maximum Shear (Vu) = 107.23 kN Shear Capacity (Vc) = 160.92 kN > Vu

0.17∗√

^′

60.9 u Bottom Slab

Maximum Shear (Vu) = 113.58 kN Shear Capacity (Vc) =

201.15

kN > Vu

(14)

Customer: SAPAC Size: L =1000 X W =800 mm & Depth from GL =4500 Side Wall

160.92

kN > Vu Final Size and Reinforcement

Box culvert Inside Dimensions = 1000 x 800 mm

0.17∗√

^′

Top Slab Thickness = 200 mm Bottom Slab Thickness = 240 mm Side Wall Thickness = 200 mm Reinforcement Dia (mm) C/C Dia (mm) C/C 10 150 10 150 10 150 10 150 Top Slab B tt Sl b

Location Inside Outside

10 150 10 150 10 150 10 150 Bottom Slab

(15)

Client:

SAPAC

(16)

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. A typical section of the culvert is shown in Figure. Material and design parameters are given in Table. 24 _kN/m3 18 kN/m3 35 Mpa 1000 mm 1000 mm 200 Material and Design Parameters

Reinforced Concrete, c Soil, s Compressive Strength, f’c Span L Rise R T Sl b Thi k Tt 200 mm 240 mm 4500 mm 200 mm 50 mm 40 mm 420 Mpa 27789.4 Mpa Haunch Thickness, Th Top Slab Thickness, Tt Bottom Slab Thickness, Tb Height of Fill H

Wall Thickness, Ts

Reinforcement Clear Cover Yield Strength, fy

Modulus Elasticity of Concrete, E

27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, E

s 200000 Mpa

(17)

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 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

5.86

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.

Dcbottom = 36.28 kN (for 1 m wide)

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 outside width of the culvert (Bc):

(18)

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 at-rest conditions a maximum stage full soil unit weight and a minimum stage half soil unit weight 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:

rest conditions, a maximum stage full soil unit weight and a minimum stage half soil unit weight will be are used.

= 106.92 kN/m (Bottom)

= 53.46 kN/m (Bottom)

Use an active coefficient of lateral earth pressure ka 0.2827

The height is:

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:

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

(19)

heq = 0.77 m

kN/m

5940 mm

Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq = 2.05ft

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.

heq = 0.63 m

At the inside of the culvert, the lateral water pressure is:

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:

WAtop = 0 kN/m2

9.81 kN/m2

E. Live Load

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)

Th d i li l d i l d th HL 93 t k d t d l d Si th f th b l t i Dynamic Load Allowance

-27.885 = 0 The dynamic load allowance may not be taken less than zero.

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.

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:

(20)

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.

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

where Pw = 130kN

Axlespacing = 1.8m

A single 3 Axle with 600 kN Truck configuration produces a live load intensity of: 1.20 is used for strength and service limit states.

Wtire = 0.51m W = 7.49 m Ltire = 0.25m L= 7.23 m Therefore WLL+IM = 5.77 kN/m

(21)

A tandem truck axle configuration produces a live load intensity of: where Pw = 105 kN 6.73 m where Axlespacing = 1.3m WLL+IM = 10.01 kN/m therefore W = 10 01 kN

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.

therefore WLL+IM = 10.01 kN

Final Loading

DC = Sel weight of Culvert DC bottom reaction = 36.28 kN/m EV = 133.07 kN/m EHTmax = 81.00 kN/m EHBmax = 106.92 kN/m EHTmin = 40.50 kN/m EHBmin = 53.46 kN/m LLStop = 3.91 kN/m LLSbottom = 3.18 kN/m WAtop= 0 kN/m WAbottom= 9.81 kN/m WAbottomreaction= 8.18 kN/m LL+IM 10 01 kN/ LL+IMW = 10.01 kN/m F. Load Combination Strength Limit states

(22)

1 Maximum Vertical Load and Maximum Horizontal Load 1.00 DC + 1.00 EV + 1.00 (LL+IM)+1.00EH.00 C .00 .00 ( ) .00 maxmax + 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

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

li d h l ( h li l d) d b i d b if i l

where

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.

where, F = 1 fy = 420 Mpa fc' = 35 MPa b = 1 m therefore, a = As x 420 0.85 x 35 x1000 a= 0.0141 As Mu = 1 x As x 420 x (d - .0141 * As/2) Mu = 420 x As*d - 2.961 As^2

420∗

√ 176400 ^2 11.844

/5.922

(23)

Side Wall

d= 155 mm As = 267.40 mm2 Minimum sidewall flexural reinforcement

Asmin = 0 002 x b x Ts = 400 00 mm2 Asmin = 0.002 x b x Ts = 400.00 mm2 therefore As = 400.00 mm2

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2 Inside Mu = 13.237 kNm Main bar dia = 10 mm

Asmin = 0.002 x b x Ts = 400.00 mm2 therefore As = 400.00 mm2

(24)

Top Slab

Max @ Mid Slab @IS

Max @ Slab End @OS

Asmin = 0.002 x b x Tt = 400.00 mm2 therefore As = 430.81 mm2

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2 Outside Mu = 6.618 kNm Main bar dia = 10 mm

d= 155 mm d= 155 mm As = 102.13 mm2 Minimum sidewall flexural reinforcement

(25)

Bottom Slab

Asmin = 0.002 x b x Tb = 480.00 mm2 therefore As = 480.00 mm2

for 1 m length 10 mm dia X 6.67 Pcs 523.60 mm2 Outside Mu = 13.623 kNm Main bar dia = 10 mm

d= 195 mm d= 195 mm As = 167.35 mm2 Minimum sidewall flexural reinforcement

(26)

Checking of Shear Top Slab

160.92

kN > Vu

0.17∗√

^′

Bottom Slab

201.15

kN > Vu

(27)

Side Wall

160.92

Box culvert Inside Dimensions = 1000 x 1000 mm Top Slab Thickness = 200 mm

0.17∗√

^′

Bottom Slab Thickness = 240 mm Side Wall Thickness = 200 mm Reinforcement Dia (mm) C/C Dia (mm) C/C 10 150 10 150 10 150 10 150 10 150 10 150 Top Slab Bottom Slab Side Wall

(28)

Client:

SAPAC

(29)

Introduction:

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

24 _kN/m3 18 kN/m3 35 Mpa 3000 mm 1500 mm 320 mm 360 mm

Material and Design Parameters

Reinforced Concrete, c

Soil, s

Compressive Strength, f’c

Span L Rise R

Top Slab Thickness, Tt

Bottom Slab Thickness Tb 360 mm

4500 mm 320 mm 50 mm 40 mm 420 Mpa 27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, E

s 200000 Mpa

Modulus Elasticity of Concrete, E

c Haunch Thickness, Th

Bottom Slab Thickness, Tb Height of Fill H

Wall Thickness, Ts Reinforcement Clear Cover Yield Strength, fy

(30)

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

14.13

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.

1.25

The interaction factor for embankment conditions is dependent on the height of fill (H) and the outside width of the culvert (Bc):

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

(31)

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 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: used.

= 120.24 kN/m (Bottom)

= 60.12 kN/m (Bottom)

Use an active coefficient of lateral earth pressure ka = 0.2827

The height is:

p

(32)

heq = 0.77 m

kN/m

6680 mm

Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq = 2ft

heq = 0.61 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.

eq

14.72 kN/m2

E. Live Load

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

(Span + Ts)

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:

(33)

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.

where Pw = 130kN

Wtire = 0.51m

g

tire W = 7.49 m Ltire = 0.25m L= 7.23 m Therefore WLL+IM = 5.77 kN/m

(34)

A tandem truck axle configuration produces a live load intensity of: where Pw = 105 kN 6 73 6.73 m where Axlespacing = 1.3m WLL+IM = 10.01 kN/m therefore WLL+IM = 10.01 kN

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.

Final Loading

DC = Sel weight of Culvert DC bottom reaction = 66.23 kN/m 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 LLStop = 3.91 kN/m LLSbottom = 3.10 kN/m WAtop= 0 kN/m WAbottom= 14.72 kN/m WAbottomreaction= 13.30 kN/m LL+IMW = 10.01 kN/m F. Load Combination Strength Limit states

(35)

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

where,

F = 1 fy = 420 Mpa fc' = 35 MPa

thickness of members near each corner.

fc' = 35 MPa b = 1 m therefore, a= 0.0141 As Mu = 1 x As x 420 x (d - .0141 * As/2) Mu = 420 x As*d - 2.961 As^2 a = As x 420 0.85 x 35 x1000

√

420∗

√ 176400 ^2 11.844

/5.922

(36)

Side Wall

d= 272 mm As = 1,064.84 mm2 Minimum sidewall flexural reinforcement

Asmin = 0.002 x b x Ts = 640.00 mm2 therefore As = 1 064 84 mm2

therefore As 1,064.84 mm2

for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2 Inside Mu = 64.1 kNm Main bar dia = 16 mm

(37)

Top Slab

Asmin = 0.002 x b x Tt = 640.00 mm2 therefore As = 1,257.83 mm2

for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2 Outside Mu = 68.21 kNm Main bar dia = 14 mm

d= 273 mm As = 604 32 mm2 As = 604.32 mm2 Minimum sidewall flexural reinforcement

(38)

Bottom Slab

(39)

Maximum Shear (Vu) = 262.78 kN Shear Capacity (Vc) = 281.61 kN > Vu Bottom Slab

0.17∗√

^′

Bottom Slab

0.17∗√

^′

321.83

(40)

Side Wall

281.61

Box culvert Inside Dimensions = 3000 x 1500 mm Top Slab Thickness = 320 mm Bottom Slab Thickness = 360 mm

id ll hi k 320

0.17∗√

^′

Side Wall Thickness = 320 mm Reinforcement Dia (mm) C/C Dia (mm) C/C 16 150 14 150 16 150 14 150 16 150 16 150 Top Slab Bottom Slab Side Wall

(41)

Client:

SAPAC

(42)

Introduction:

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

24 _kN/m3 18 kN/m3 35 Mpa 2500 mm 1000 mm 280 mm 320 mm

Reinforced Concrete, c

Soil, s

Compressive Strength, f’c

Span L Rise R

Top Slab Thickness, Tt

Bottom Slab Thickness Tb 320 mm

4500 mm 280 mm 50 mm 40 mm 420 Mpa 27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, E

s 200000 Mpa

Modulus Elasticity of Concrete, E

c Haunch Thickness, Th

Bottom Slab Thickness, Tb Height of Fill H

Wall Thickness, Ts Reinforcement Clear Cover Yield Strength, fy

(43)

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

8.74

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.

1.29

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

(44)

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 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: used.

= 109.80 kN/m (Bottom)

= 54.90 kN/m (Bottom)

The height is:

p

(45)

heq = 0.77 m

kN/m

6100 mm

Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is: heq = 2ft

heq = 0.61 m

eq

9.81 kN/m2

E. Live Load

(Span + Ts)

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:

(46)

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.

where Pw = 130kN

Wtire = 0.51m

g

tire W = 7.49 m Ltire = 0.25m L= 7.23 m Therefore WLL+IM = 5.77 kN/m

(47)

A tandem truck axle configuration produces a live load intensity of: where Pw = 105 kN 6 73 6.73 m where Axlespacing = 1.3m WLL+IM = 10.01 kN/m therefore WLL+IM = 10.01 kN

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.

Final Loading

DC = Sel weight of Culvert DC bottom reaction = 53.44 kN/m 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 LLStop = 3.91 kN/m LLSbottom = 3.10 kN/m WAtop= 0 kN/m WAbottom= 9.81 kN/m WAbottomreaction= 8.82 kN/m LL+IMW = 10.01 kN/m F. Load Combination Strength Limit states

(48)

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

where,

F = 1 fy = 420 Mpa fc' = 35 MPa

thickness of members near each corner.

fc' = 35 MPa b = 1 m therefore, a= 0.0141 As Mu = 1 x As x 420 x (d - .0141 * As/2) Mu = 420 x As*d - 2.961 As^2 a = As x 420 0.85 x 35 x1000

√

420∗

√ 176400 ^2 11.844

/5.922

(49)

Side Wall

Asmin = 0.002 x b x Ts = 560.00 mm2 therefore As = 913 02 mm2

therefore As 913.02 mm2

for 1 m length 14 mm dia X 6.67 Pcs 1,026.25 mm2 Inside Mu = 53.33 kNm Main bar dia = 14 mm

(50)

Top Slab

Asmin = 0.002 x b x Tt = 560.00 mm2 therefore As = 1,047.62 mm2

(51)

Bottom Slab

for 1 m length 16 mm dia X 6.67 Pcs 1,340.41 mm2 Outside Mu = 82 kNm Main bar dia = 12 mm

(52)

Maximum Shear (Vu) = 225.17 kN Shear Capacity (Vc) = 241.38 kN > Vu Bottom Slab

0.17∗√

^′

Bottom Slab

0.17∗√

^′

281.61

(53)

Side Wall

241.38

Box culvert Inside Dimensions = 2500 x 1000 mm Top Slab Thickness = 280 mm Bottom Slab Thickness = 320 mm

id ll hi k 280

0.17∗√

^′

Side Wall Thickness = 280 mm Reinforcement Dia (mm) C/C Dia (mm) C/C 16 150 12 150 16 150 12 150 14 150 14 150 Top Slab Bottom Slab Side Wall

(54)

Client:

SAPAC

BOX CULVERT SIZE 3000 X 1000

(55)

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.yp g g p g

24 _kN/m3 18 kN/m3 35 Mpa 3000 mm 1000 mm 320 mm 360 mm 4500 mm Reinforced Concrete, c Soil, s Compressive Strength, f’c Span L Rise R

Top Slab Thickness, Tt Bottom Slab Thickness, Tb Height of Fill H 320 mm 50 mm 40 mm 420 Mpa 27789.4 Mpa

Modulus Elasticity of Steel Reinforcement, E

s 200000 Mpa

Modulus Elasticity of Concrete, E

c

Haunch Thickness, Th Wall Thickness, Ts Reinforcement Clear Cover Yield Strength, fy

(56)

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

to the calculations to convert the units to kN/m for consistency with national conventions.

A. Dead Load

10.29

0.03 kN (for 1 m wide)( )

B E th P L d

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.

1.25

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

(57)

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:

111 24 kN/m (B tt )

used.

= 111.24 kN/m (Bottom)

= 55.62 kN/m (Bottom)

The height is:

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

(58)

By interpolation, the equivalent height for a fill depth of 4500 mm is:

h_eq = 2.52ft

h_eq = 0.77 m

kN/m

6180 mm

Again using interpolation and AASHTO Table 3.11.6.4.1, the equivalent height is:

h_eq = 2.03ft

h_eq = 0.62 m

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

kN/m

D. Water Load

At the inside of the culvert, the lateral water pressure is:

WA_top = 0 kN/m2

9.81

kN/m2

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:

E. Live Load

Wabottom reaction = WA bottom * Span = 8.86 kN/m (Span + Ts)

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.

-27.885 = 0

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

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: