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TYPICAL CALCULATION OF LIVE LOAD REACTION FOR PIER SUBSTRUCTURE

FOR SIMPLY SUPPORTED SPANS OF A THREE LANE BRIDGE STRUCTURE

Centre line of pier w.r.t. the bearings :-

Rb = 0.3 m

Rc = 0.3 m

Reaction has been calculated for the following cases

1. One lane of class 70-R(W)

2. One lane of class - A

3. Two lane of class - A

4. Three lane of class - A

5. One lane of class 70-R(W) + One lane of class - A

Condition A: MAXIMUM LONGITUDINAL MOMENT CASE

Case 1: One lane of class 70-R(W)Cg of 100 t

5.12

0.3 m 18.80 m Rb Rc 18.80 m 0.30 m

Ra 0.30 m 0.30 m Rd

Rb = 100*(18.8-5.12+0.3)/18.8 = 81.3 t

Rc = = 0.0 tRa= = 18.7 t

Vert.Reaction= 81.3 + 0 = 81.3 t

Braking Force, B = 0.2*100 = 20.0 t

Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 20.0 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL of 70-R CL of c/w

2.595 2.905

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B) One lane of class-A

Cg of 55.4t

9.7 0.0

0.3 m 18.80 m Rb Rc 18.80 m 0.3 mRa 0.30 m 0.30 m Rd

Rc = 0*(18.8-0.3)/18.8 = 0.0 t

Rb = 55.4*(18.8-9.7+0.3/2)/18.8 = 27.7 t

Ra= = 27.7 t

Vert.Reaction = 0 + 27.7 = 27.7 t

Braking Force, B = 0.2*(0+55.4) = 11.1 t

Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 11.1 t( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class A(1L) CL of c/w

1.30

11 m

Transverse eccentricity = 4.20 m

Transverse moment = 4.2*27.7 = 116.3 t.m

Long. moment = 27.7*0.3-0*0.3 = 8.3 t.m

Long. Eccentricity ( for input) = 0.300 m

Case 3 : Two lane of class-A

Rc = 2*0 = 0.0 t

Rb = 2*27.7 = 55.4 t

Ra= = 55.4 t

Vert.Reaction = 0 + 55.4 = 55.4 t

Braking Force(For single lane only) = 11.1 t

Dead load reaction on the pier , Rg = 410.0 tValue of " m " = = 0.00

Horizontal force due to temperature T = m*(Rg+Ra) = 0 0 t

4.20

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Case 4 : Three lane of class-A

Rc = 90% of 3*0 = 0.0 t

Rb = 90% of 3*27.7 = 74.8 t

Ra= = 1.3 t

Vert.Reaction = 0 + 74.8 74.8

Braking Force, B = (0.2)*55.4+0.05*55.4 = 13.9 t

(5% extra taken for third lane)Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 13.9 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class A(3L) CL of c/w

0.7

11 mTransverse eccentricity = 0.70 m

Transverse moment = 0.7*74.8 = 52.4 t.m

Long. moment = 74.8*0.3-0*0.3 = 22.4 t.m

Long. Eccentricity ( for input) = 0.300 m

Case 5 : One lane of class-70R(W)+One lane of class-A

Rc = 90% of(0+0) = 0.0 t

Rb = 90% of(27.7+81.28) = 98.1 t

Ra= = 41.8 t

Braking Force = 20 + 5% of 55.4 = 22.8 t

(5% extra taken for class A)

Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 22.8 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class 70-R CL of c/w CL class A(1L)

2.595 0.84

4.80

2.905

11 0 m

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Condition B: MAXIMUM TRANSVERSE MOMENT / REACTION CASE

CASE 1: ONE LANE OF CLASS 70-R(W)

cg 100.0 t Cg of 51.0

Cg of 49.0 t

0.3 m 18.80 m Rb Rc 18.80 m

Ra 0.30 m 1.60 m Rd

Rb = 49*(18.8 - 3.33 + 0.3)/18.8 = 41.10 t

Rc = 51*(18.8-3.19+1.6)/18.8 = 38.01 t

Ra= = 11.0 t

Vert. Reaction = 41.1 + 38 = 79.0 t

Braking Force, B = 0.2*100 = 20.0 t

Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 20.0 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL of 70-R CL of c/w

2.595

11 m

Transverse eccentricity = 2.905 m

Transverse moment = 2.905*(41.1 + 38) = 229.5 t.m

Long. moment = 41.1*0.3-38.01*0.3 = 0.9 t.m

Long. Eccentricity ( for input) = 0.012 m

Case 2: One lane of class-A

Cg of 28.2 55.4 t Cg of 27.20 t

9.09 9.71 m

4.07 5.02 5.21 4.5 m

5.12

3.19

3.33

1.60m

2.905

Cg of

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Case 3 : Two lane of class-A

Rc = 2*20.1 = 40.2 t

Rb = 2*21.1 = 42.2 t

Ra= = 14.2 t

Vert.Reaction = 40.2 + 42.2 = 82.4 tBraking Force(For single lane only) = 11.1 t

Dead load reaction on the pier , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 11.1 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class A(2L) CL of c/w

3.05

11 m

Transverse eccentricity = 2.45 m

Transverse moment = 2.45*82.4 = 202.0 t.m

Long. moment = 42.2*0.3-40.2*0.3 = 0.6 t.m

Long. Eccentricity ( for input) = 0.007 m

Case 4 : Three lane of class-A

Rc = 90% of 3*20.1 = 54.3 t

Rb = 90% of 3*21.1 = 57.0 t

Ra= = 19.1 t

Vert.Reaction = 54.3 + 57 111.3

Braking Force, B = (0.2)*55.4+0.05*55.4 = 13.9 t

(5% extra taken for third lane)

Dead load reaction on the pier end , Rg = 410.0 t

Value of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 13.9 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class A(3L) CL of c/w

0 7

2.45

4 80

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Case 5 : One lane of class-70R(W)+One lane of class-A

Rc = 90% of(20.1+38.01) = 52.3 t

Rb = 90% of(21.12+41.1) = 56.0 t

Ra= = 20.1 t

Braking Force = 20 + 5% of 55.4 = 22.8 t

(5% extra taken for class A)

Dead load reaction on the pier , Rg = 410.0 tValue of " m " = = 0.00

Horizontal force due to temperature, T = m*(Rg+Ra) = 0.0 t

Design horizontal force is higher of either ( B/2+T ) or ( B-T ) = 22.8 t

( neglecting shear rating of elastomeric bearing in the adjacent span, which is on the conservative side )

CL class 70-R CL of c/w CL class A(1L)

2.595 0.84

Transverse ecc.(class 70 R) = 2.905 mTransverse ecc.(class A) = -0.84 m

Trans. moment = 0.9*(81.3*2.9-0*-0.8) = 175.4

Net transverse ecc. (for input) = 1.620 t.m

Long. moment = 56*0.3-52.3*0.3 = 1.1 t.m

Long. Eccentricity ( for input) = 0.010 m

2.905

11.0 m

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first span

SPAN LOAD CG

8.28 49 3.33

5.04 58 2.18

19.40

second span

4.4 34 3.715

5.12 51 3.19

22.00

two span length load cg6.8 end cg2.7 end9 27.2 4.5 4.5

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28.2 4.07 18.2 1.81

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span load cg

4.42 51 1.93

5.79 68 2.8957.92 80 3.65

9.44 92 4.4

13.4 100 5.12

19.23

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SPAN LOAD CG

5.5 29.6 1.73

8.5 36.4 2.99

11.5 43.2 4.33

14.5 50 5.71

24 50 5.71

19.23

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second span

SPAN LOAD CG

3 80 3.65

4.52 92 4.4

8.48 100 5.1224 100 5.12

19.40

first span

3 17 0.87

4.52 29 1.75

8.48 41 2.56

24 49 3.53

19.40

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Summary of Loads

Max.

vertical

reaction (t)

81.3 2.905 0.300

27.7 4.200 0.300

55.4 0.700 0.30074.8 0.700 0.300

98.1 1.953 0.300

Max.

vertical

reaction (t)

Transverse

moment

(t.m)

Longitudinal

moment (t.m)

1L class 70 - R 79.0 229.5 0.9 20.0 2.905 0.012

1L class - A 41.2 173.1 0.3 11.1 4.200 0.0072L class - A 82.4 202.0 0.6 11.1 0.614 0.007

3L class - A 111.3 77.9 0.8 13.9 0.700 0.007

108.3 175.4 1.1 22.8 1.620 0.010

Transverse

ecc. (m)

Longitudinal

ecc. (m)

Transverse

ecc. (m)

Longitudinal

ecc. (m)

20.0

22.8

11.1

11.113.9

135.7

116.3

1L class 70 - R +

1L class - A

191.6

Load case

29.4

Max.Transverse Moment

52.4 22.4

8.3

Vertical reaction d ue to braking has been neglected.

Transverse moment

(t.m)

16.6

24.4

Design horizontal force

(t)

Max. Longitudinal Moment

Design

horizontal

force (t)

Longitudinal moment (t.m)

236.1