CHAPTER 3

3.0 BRIDGE DECK MODELING, ANALYSIS AND PRESTRESSED DESIGN

3.1 BEAM SECTION SELECTIONS

1 . STANDARD BOX BEAM SECTION

For the 30m Span, The standard box beam B14 is selected from the PCDG table. It has the beam

height of 1360mm and the width of 970mm.Its Properties are as table 3 .1 . For the proposed

four lane deck, 17 numbers of beams are required. The beam arrangements are shown in figure

3.1 .

Table 3.1 Standard box beam properties

Parameters values Area 651001 m m 2

Centroid above bottom 649 mm Section modulus top 199.30 * 1 0 6 m m 3

Section modulus bottom 199.30 * 1 0 6 m m 3

Self weight 15.34 kN/m

3L r-1200- i

& 5k, r-110O-ij

V — V V V V V V V V v — V _V i 55

Figure 3.1 Bridge deck arrangement for standard box beam

2. STANDARD U BEAM SECTION

For the 30m Span, The standard box beam U l l is selected from the PCDG table. It has the beam

height of 1500mm and the width of 970mm. Its Properties are as table 3.2. For the proposed

four lane deck, 10 numbers of beams are required. The beam arrangements are shown in figure

3.2. Beams are kept at 1750mm intervals.

17

Table 3.2 Standard U beam properties

Parameters values Area 697450 m m 2

Centroid above bottom 689 mm Section modulus top 210.50 * 1 0 6 m m 3

Section modulus bottom 247.90 * 1 0 6 m m 3

Self weight 16.46 kN/m Second moment of area 170.76 * 1 0 9 m m 4

Figure 3.2 Bridge deck arrangement for standard U beam

3. SPACED RECTANGULAR BOX BEAM SECTION

For the 30m Span, The selected beam has the beam height of 1300mm and the width of

1040mm. Its Properties are as in table 3.3. For the proposed four lane deck, 11 numbers of

beams are required. The beam arrangements are shown in figure 3.3. These beams have been

kept at 1540 mm spacing such that there is a 500 mm clear spacing between beams.

Table 3.3 Spaced box beam properties

Parameters values Area 651200 m m 2

Centroid above bottom 650 mm Section modulus top 196.77 * 1 0 6 m m 3

Section modulus bottom 196.77 * 1 0 6 m m 3

Self weight 15.63 kN / m Second moment of area 127.9 * 1 0 9 m m 4

18

LIBRARY UllVfcRSITY Of MORATUWA. SRI IANX.

IWTO

• JJOD j

*• )

y T / \ /

f — V

l T / \

' .-K 500

Figure 3.3 Bridge deck arrangement for spaced rectangular box beam

4. SPACED TRAPEZOIDAL BOX BEAM SECTION

For the 30m Span, The selected trapezoidal box beam has been used in a four lane bridge. The

beam height of 1300mm and the top width of 3500mm are adapted. For the four lane deck only

4 numbers of beams are required. The beam arrangements are shown in figure 3.4.

qoo I «oo ^ «aoo

Figure 3.4 Bridge deck arrangement for spaced trapezoidal box beam

3.2. SPECIMEN CALCULATIONS FOR GRILLAGE MODELLING AND BRIDGE LOADINGS

For the specimen calculation, the spaced rectangular box beam has been used here. For the

grillage analysis, SAP 2000 general purpose structural package was used. SAP 2000 allows the

use of frame elements to model the behavior of beams with six degrees of freedom at each

end. This includes biaxial bending, torsion, axial deformation, and biaxial shear deformations.

Thus, the frame elements can be used to model planar grillages. For the grillage modeling

prismatic members have been used. The material properties include modulus of elasticity,

torsional stiffness, the coefficient of thermal expansion, the mass density for computing

element mass and weight density for computing the self weight. The geometric properties

include the cross sectional area, the moment of inertia about two perpendicular axes, the

torsional constant, the shear areas for transverse shear. In order to take account of factors that

cannot be easily described in geometry, the property set modifiers can be used.

3.2.1 GRILLAGE MODELLING PARAMETERS

1 . LONGITUDINAL COMPOSIT INTERMEDIATE BEAM ELEMENT

1540

220

579

250

4

821

1040

Figure3.5 Intermediate beam section

Composite area = 0.8802 m 2

Set modifiers for area = 1.134

Second moment of area about centroid axis l x x=0.2025 m 4

Set modifiers for lXx= 1.118

2. TORSION CONSTANT-C

1 2 3 0 ^ 1(10

1040

- 2 2 6 -

180

8 6 0

1400

Figure3.6 Idealized intermediate beam section

20

For top slab cantilever portion, say Q

B m a x / b = 2 5 0 / 2 5 0 = 1

K= 0 . 1 4 1

d = k b 3 b M A X * 0 . 5 = 0 . 1 4 1 * 0 . 2 5 3 * 0 . 2 5 * 0 . 5 = 2 . 7 5 4 * 1 0 " 4 m 4

For both side it is factored by 2

For rectangular hollow section, say C 2

C 2 = 4 A 7 ( J d s / 1 ) = 4 * ( 1 2 3 0 * 8 6 0 ) 2 / ( 8 6 0 / 1 2 0 + 8 6 0 / 2 2 0 + 1 2 3 0 / 1 8 0 )

= 1 . 8 0 8 9 * 1 0 1 1 m m 4

= 0 . 1 8 1 m 4

Total torsion constant = 2 . 7 5 4 * 10" 4 * 2 + 0 . 1 8 1 m 4

= 0 . 1 8 1 3 m 4

Set modifiers for C= 0 . 9 3 4

3. LONGITUDINAL COMPOSIT EDGE BEAM ELEMENT

1770

2SO

J . 2SO

\ )

480

\ )

480

841

\ )

Figure 3 . 7 Edge beam section

21

Composite area = 0.9377 m

Set modifiers for area = 1.208

Second moment of area about centroid axis l x x=0.214 m 4

Set modifiers for lXx= 1.18

4. TORSION CONSTANT-C

The idealized section has been considered.

1 0 4 0

1 2 3 0 ^

1 4 0 0

Figure 3.8 Idealized edge beam section

For top slab cantilever portion one side, say Ci

Bmax/ b = 250/250=1

K= 0.141

Ci=k b3bm ax*0.5= 0.141 * 0.253 *0.25*0.5=2.754*104 m 4

For other side, say C2

B m a x / b = 480/250=1.92

22

K= 0.224

Ci=k b 3 b m a x * 0 . 5 = 0.224 * 0.25 3 *0 .48*0.5=8.4*10 4 m 4

For rectangular hollow section, say C 2

C 2 =4A 2 / ( J d s /1)=4 * (1230*860) 2 / (860/120 +860/220 +1230/180)

=1.8089 * 1 0 1 1 m m 4

=0.181 m 4

Total torsion constant = 2.754* 10 4 + 8.4* 10"4 +0.181 m 4

= 0 . 1 8 2 1 m 4

Set modifiers for C= 0.938

5. TRANSVERSE SLAB ELEMENTS

Edge slab beam

250

500

Figure 3.9 Edge slab beam

Second moment of area about composite centroid = l 0 + AX2=0.0264 m 4

Set modifiers for I = 40.55

For torsion constant, say Ci

B m a x / b = 500/250=2

K= 0.229

Ci=k b 3 b m a x * 0 . 5 = 0.229 * 0.25 3 * 0 .50 *0 .5=1 .789*10 4 m 4

23

For intermediate slab beams

^ 7 V-

N

250 V

Figure 3.10 Intermediate slab beam

Second moment of area about composite centroid I = l 0 + AX2=0.0528 m 4

Set modifiers for I = 40.55

Torsion constant will be calculated by SAP 2000, but to be used a set modifier of 0.5 since the

slab will be used in both longitudinal and transverse bending.

3.2.2. LOADINGS

1. HA loadings

HA loading for 30m long beam as uniformly distributed load = 30 KN /m/per lane

Knife edge load = 120 KN per lane loaded at critical location

HA loading was applied at each lane of 3.5 m of width. This will give a value of 30/3.5 =8.57

KN/m 2 . This was allocated to the longitudinal members. A tributary area was calculated

considering the relative locations of longitudinal members and the location of lanes. It is

ensured that the addition of all load components will add up to 30 KN/m. These were applied in

lane 1,2,3 and 4 with the names of hal,ha2,ha3 and ha4 respectively. The HA load is shown in

figure 3.11.

For knife edge loads, they can be applied to maximize the flexure or shear. For flexure, they are

applied close to the centre as kelbl , kelb3 and kelb4 on each corresponding lane. For shear,

they are applied close to the support as kelsl, kels2, and kels4 on each lane.

2. PEDESTRIAN LOAD

Since there are four lanes as per clause 7.2.1 of BS5400:Part4, half of the load can be

considered, = 0.5 *5=2.5 KN /m 2 .This is applied on both pedestrian walks as ped l and ped2.

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3. HB LOADING

25

HB loading was considered as four loads spaced at 1.0m per axel, with double axels at front and

rear. The distance between the double axel is 1.8m. The clear distance between front and rear

axle was considered as 6.0m since the beams are designed as simply supported.

HB loading was also applied on the longitudinal members. HB vehicle is provided a clearance of

0.25m from the curb. The load per wheel was taken as 1.0KN. This means, axle has a load of

4KN. Since the HB vehicle has 4 axles, the total load from the vehicle is 16 KN with each wheel

carrying unit load. This will allow dealing with different intensities of HB vehicle with the same

load case. For 30 units of HB, it should be multiplied by 1200/16=75. With 1.1 partial factor of

safety, it will be 82.5.

The location of HB vehicle is very important to get maximum bending moments. The HB vehicle

is located so that its centroid will be at equal distance to one wheel of the front axle from the

centriod of the span. In this way, when the HB vehicle is located as close as foot walk, it is

named as h b l . When it is located close to central reserve, it is named as hb2.

The HB load is shown in figure 3.12.

4. DEAD LOADS

Beam dead load = 15.63 KN/m

Insitu concrete at intermediate beam= 5.5 KN/m

Insitu concrete at edge beam=6.9 KN/m

Screed concrete thickness varies from 0.00 m at foot walk curb to 0.117m at centre median

curb. Its weight varies from 0.9 kN/m at edge beam to 4.4 kN/m at mid beam.

5. SUPER IMPOSED DEAD LOADS

Centre median load = 11.4 KN/m

Foot walk load = 7.4KN/m

Hand rails = 0.65 KN/m.

Wearing surface load= 1.74 kN/m on each beam

Figure 3.11 HA udl on lane one, ha l

Figure 3.12 HB load for maximum moments on lane close to edge,hbl.

Figure 3.13 Pedestrian load,pedl

3.2.3. LOAD COMBINATIONS

In load combinations, HA alone and the HA and HB both has been considered according to BS

5400: Part 2, 1978. Those combinations used in SAP2000 grillage models are as followings since

the beam is designed as c lass ! member.

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1 . COMBINATION!

For HA loading, two lanes are loaded fully and the other lanes are loaded by 1/3 of HA. The

partial safety factor for loading under service condition was 1.2. For this, the h a l and ha2 were

considered as 1/3*1.2=0.399, and ha3 and ha4 as 1.2. The pedestrian load was considered as

1.2 p e d l and 1.2ped2. The knife edge loads were 0.399 kelbl , 0.399kelb2, 1.2kelb3 and

1.2kelb4.

COMB1=0.399 (hal+ha2) +1.2(ha3+ha4) + 0.399(kelbl+kelb2) +1.2 (kelb3+kelb4) +1.2

(pedl+ped2).

2. C O M B I N A T I O N

For HA and HB loadings, two lanes are loaded with HB, such that it moves in the lane close to

the foot walk and the other lanes are loaded by 1/3 of HA. The partial safety factor for loading

under service condition was 1.1. For this, the h a l and ha2 were considered as 1/3*1.1=0.366,

and h b l as 1.1. The pedestrian load was considered as 1.1 ped l and l . lped2 . The knife edge

loads were 0.366 kelbl , 0.366kelb2.

COMB2=0.366 (hal+ha2) +82.5 (hbl) + 0.366(kelbl+kelb2) +1.1 (pedl+ped2).

3. COMBINATIONS

For HA and HB loadings, two lanes are loaded with HB, such that it moves as close as to the

central reserve and the other lanes are loaded by 1/3 of HA. The partial safety factor for loading

under service condition was 1.1. For this, the h a l and ha2 were considered as 1/3*1.1=0.366,

and hb2 as 1.1. The pedestrian load was considered as 1.1 p e d l and l . lped2 . The knife edge

loads were 0.366 kelbl , 0.366kelb2.

COMB3=0.366 (hal+ha2) +82.5 (hb2) + 0.366(kelbl+kelb2) +1.1 (pedl+ped2).

4.COMBINATION FOR M A X I M U M SHEAR

For HA loading, two lanes are loaded fully and the other lanes are loaded by 1/3 of HA. The

partial safety factor for loading under service condition was 1.2. For this, the h a l and ha2 were

considered as 1/3*1.2=0.399, and ha3 and ha4 as 1.2. The pedestrian load was considered as

1.2 ped l and 1.2ped2. The knife edge loads for maximum shear were 0.399 kelsl, 0.399kels2,

1.2kels3 and 1.2kels4.

MSHCOMB1=0.399 (hal+ha2) +1.2(ha3+ha4) + 0.399(kelsl+kels2) +1.2 (kels3+kels4) +1.2

(pedl+ped2).

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5. ENVELOPES

SAP2000 provides a facility to obtain the envelopes. The envelope obtained for these

combinations is named as Envelope-1. This includes all loads combinations mentioned above.

Maximum Shear forces and torsion moments have been obtained with the ultimate limit state

partial load factors according to Table 1 of BS5400: Part2:1978. Those factors are shown in

table3.4.

Table 3.4 Partial load factors for ultimate limit state

Load Name Ta­ ff3

Weight of the Beam L I S 1.10 Weight of Concrete deck 1.15 1.10

Weight of foot walk and median 1.15 1.10

Weight of wearing course 1.75 1.10

Weight of hand rail 1.75 1.10 HA Loads alone 1.50 1.10 HA Loads with HB 1.30 1.10 HB Loads 1.30 1.10 Pedestrian loads 1.50 1.10

3.3. BENDING MOMENTS, SHEAR FORCES AND TORSION MOMENTS

The maximum bending moments, shear forces and torsion moments that were got from grillage

analysis are tabulated below.

28

Table 3.5 Bending moments for edge beam (kNm)

DISTANCE(m) LIVE ENVELOPE 1 SID SCREED BEAM INSITU

1 244.10 77.50 20.10 109.41 48.30

2 427.60 143.50 43.50 320.42 141.45

3 597.20 202.50 66.80 515.79 227.70

4 754.30 256.20 88.91 695.54 307.05

5 900.60 305.10 109.40 859.65 379.50

6 1035.90 349.31 128.10 1008.14 445.05

7 1160.10 388.95 144.97 1140.99 503.70

8 1272.70 423.97 159.90 1258.22 555.45

9 1373.80 454.40 172.95 1359.81 600.30

10 1463.00 480.10 184.00 1445.78 638.25

11 1540.60 501.20 193.10 1516.11 669.30

12 1605.99 517.50 200.10 1570.82 693.45

13 1658.70 529.20 205.20 1609.89 710.70

14 1697.70 536.30 208.20 1633.34 721.05

15 1721.80 538.60 209.20 1641.15 724.50

16 1697.70 536.30 208.20 1641.15 724.50

Table 3.6 Bending moments for intermediate beam (kNm)

DISTANCE(m) LIVE ENVELOPE 1 SID SCREED BEAM INSITU

1 230.60 64.40 29.00 109.41 38.50

2 383.92 126.40 55.40 320.42 112.75

3 542.80 183.98 79.15 515.79 181.50

4 692.40 236.70 100.40 695.54 244.75

5 828.40 284.47 119.40 859.65 302.50

6 952.20 327.50 136.20 1008.14 354.75

7 1064.60 365.90 151.00 1140.99 401.50

8 1166.23 399.60 163.97 1258.22 442.75

9 1257.30 428.80 175.10 1359.81 478.50

10 1338.00 453.50 184.50 1445.78 508.75

11 1408.60 473.70 192.10 1516.11 533.50

12 1469.20 489.40 198.00 1570.82 552.75

13 1520.20 500.60 202.25 1609.89 566.50

14 1562.50 507.30 204.80 1633.34 574.75

15 1597.10 509.50 205.60 1641.15 577.50

16 1562.45 507.30 204.80 1641.15 577.50

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Table 3.7 Shear forces and Torsion moments for edge beam

DISTANCE SHEA R(KN) ORSION(kNm)

LIVE SID DEAD TOTAL LIVE SID+DEAD TOTAL

0 338.08 132.15 510.87 981.10 77.67 -2.21 75.46

1 265.26 113.90 488.36 867.52 161.86 -5.16 156.70

2 237.22 102.65 457.40 797.27 191.05 -6.36 184.69

3 219.96 94.02 423.28 737.26 198.50 -6.70 191.80

4 204.98 86.30 388.10 679.38 197.17 -6.57 190.60

5 189.90 78.84 352.55 621.29 191.64 -6.16 185.48

6 174.36 71.43 316.86 562.65 183.18 -5.59 177.59

7 162.34 64.01 281.09 507.44 171.97 -4.92 167.05

8 168.96 56.55 245.28 470.79 157.55 -4.21 153.34

9 174.73 49.07 209.43 433.23 140.29 -3.50 136.79

10 178.11 41.57 173.54 393.22 120.88 -2.80 118.08

11 147.75 34.06 137.62 319.43 101.26 -2.13 99.13

12 75.07 26.55 101.68 203.30 81.84 -1.49 80.35

13 56.11 19.05 65.72 140.88 60.20 -0.88 59.32

14 35.27 11.51 29.76 76.54 35.90 -0.29 35.61

15 31.09 3.99 6.02 41.10 7.71 0.29 8.00

16 35.27 11.51 29.76 76.54 -80.22 0.88 -79.34

17 56.11 19.03 65.72 140.86 -104.75 1.49 -103.26

18 75.07 26.55 101.68 203.30 -126.70 2.13 -124.57

19 92.74 34.06 137.62 264.42 -146.47 2.80 -143.67

20 109.62 41.57 173.54 324.73 -166.46 3.50 -162.96

21 126.08 49.57 209.43 385.08 -166.46 4.21 -162.25

22 176.87 56.55 245.28 478.70 -186.15 4.92 -181.23

23 206.61 64.01 281.09 551.71 -203.36 5.59 -197.77

24 202.17 71.43 316.86 590.46 -216.60 6.19 -210.41

25 194.74 78.84 352.55 626.13 -223.71 6.57 -217.14

26 204.98 86.30 388.10 679.38 -215.14 6.70 -208.44

27 219.96 94.02 423.28 737.26 -187.70 6.36 -181.34

28 237.22 102.65 457.40 797.27 -90.60 5.16 -85.44

29 265.26 113.90 488.36 867.52 -90.60 2.21 -88.39

30 329.54 132.15 510.87 972.56 -90.60 2.21 -88.39

30

Table 3.8 Shear forces and Torsion moments for intermediate beam

DISTANCE SHEAR(KN) TORSION(kNm) LIVE SID DEAD TOTAL LIVE SID+DEAD TOTAL

0 332.71 120.59 509.58 962.88 94.42 -4.14 90.28 1 265.45 107.26 472.60 845.31 181.29 -7.72 173.57 2 242.76 98.50 437.03 778.29 206.70 -8.40 198.30

3 221.60 91.51 402.04 715.15 211.01 -8.00 203.01 4 202.83 85.05 367.38 655.26 208.06 -7.20 200.86

5 185.99 78.59 332.96 597.54 202.40 -6.26 196.14

6 170.37 71.97 298.74 541.08 195.29 -5.32 189.97

7 155.47 65.16 264.68 485.31 186.73 -4.44 182.29

8 144.15 58.19 230.76 433.10 176.20 -3.64 172.56 9 153.81 51.08 196.95 401.84 162.73 -2.91 159.82

10 169.42 43.89 163.21 376.52 144.75 -2.27 142.48 11 143.37 36.62 129.52 309.51 119.47 -1.69 117.78

12 73.72 29.32 95.86 198.90 87.56 -1.17 86.39

13 63.32 21.99 62.28 147.59 55.19 -0.69 54.50

14 50.82 14.65 28.59 94.06 24.94 -0.23 24.71

15 63.32 7.29 5.03 75.64 -27.90 0.23 -27.67

16 73.72 14.65 28.59 116.96 -46.47 0.69 -45.78

17 85.85 21.99 62.28 170.12 -68.77 1.17 -67.60

18 99.02 29.32 95.86 224.20 -99.58 1.69 -97.89

19 112.73 36.62 129.52 278.87 -132.72 2.27 -130.45

20 126.75 43.89 163.21 333.85 -165.66 2.91 -162.75

21 170.95 51.08 196.95 418.98 -192.24 3.64 -188.60

22 196.89 58.19 230.76 485.84 -211.80 4.44 -207.36 23 181.54 65.16 264.68 511.38 -226.96 5.32 -221.64

24 185.99 71.97 298.74 556.70 -238.69 6.26 -232.43

25 202.83 78.59 332.96 614.38 -245.95 7.20 -238.75

26 221.60 85.05 367.38 674.03 -243.51 8.00 -235.51

27 242.76 91.51 402.04 736.31 -215.04 8.40 -206.64

28 265.45 98.50 437.03 800.98 -215.04 7.72 -207.32

29 285.43 107.26 472.60 865.29 -112.49 4.14 -108.35

30 300.30 120.59 509.58 930.47 -112.49 4.14 -108.35

31