# Analysis of Prestressed Concrete Box Girder Bridge

A box girder bridge is a special type of bridge in that beams have to compromise girders in the shape of empty box. Bridge construction has got a paramount importance worldwide. Box girder is achieving popularity in bridge engineering because of its stability, economy, structural efficiency.

## Calculation of Ultimate Strength

### (a) Failure by yield of steel (under-reinforced section)

Mult = 0.9dbAsFp

Here,

As = the area of high tensile steel

Fp = the ultimate tensile strength for steel without definite yield point or yield stress or stress at 4 per cent elongation whichever is higher for steel with a definite yield point.

db = the depth of the beam from the maximum compression edge to the centre of gravity of the steel tendons.

### (b) Failure by crushing concrete

Mult = 0.176 bdb2fck

Where,

1. b = the width of rectangular section or web of beam

2. fck= characteristics strength of concrete

3. G = Calculation of Section un- cracked in flexure

4. b = width in the case of rectangular member and width of the rib in the case of T, I and L beams

5. d = overall depth of the member

6. fcp = compressive stress at centroidal axis due to prestress taken as positive.

### (c) Analysis and Design of Post-Tensioned Deck type Box-Girder Bridge

A post- tensioned deck type Box – Girder

Bridges of clear span 30m and width of roadway is 7.5m. Assume Live Load as per IRC: 6-2000 vehicle is passing over deck given in the chapter 4. The Bridge analysis for different L/d ratio starting from 15 to 20 and different L/d ratio considered are as follows:

Case 1 L/d= 19, d = 1.6

Case 2 L/d =18, d = 1.7

Case3 L/d = 17, d = 1.8

Case4 L/d= 16, d= 1.9

Case5 L/d= 15, d=2.0

**Preliminary Data**

1. Clear span = 30m

2. Width of roadway = 7.5 m

3. Overhang from face of girder = 1.2m

4. Deck thickness = 0.2 m

5. Bottom slab thickness = 0.2 m

6. Girder thickness = 0.3 m

7. The tendon profile is considered as parabolic in nature.

**As per IRC:18-2000**

f_{ck}= 50 Mpa,

f_{ci} = 0.8

f_{ck} = 40 Mpa,

f_{ct} = 0.5

f_{ci} = 20 Mpa,

f_{cw} = 0.33

f_{ck} = 16.5 Mpa

f_{t} = 1/10

f_{ct} = 2.0 Mpa

f_{tw} = 0

**As per IS:1343-1980**

E_{c} = 5700

f_{ck}1/2 = 40.30 kN/m2

f_{p} = 1862 Mpa,

n = 0.85,

E = 2×105 Mpa

### Validation of Results

Table of Calculation of Prestress Losses - (As per IS:1343-1980)

Span (m) | ^S | ^C | ^E | ^A | ^F | ^R | Total | n |

0.0L | 8E-05 | 0.0 | 0.0 | 0.0 | 0.0 | 90 | 90 | 0.95 |

0.0L | 2.6 | 2.3 | 78 | 9.7 | 90 | 182.6 | 0.9 | |

0.0L | 2.6 | 2.4 | 39 | 22 | 90 | 155.8 | 0.91 | |

0.3L | 2.6 | 2.4 | 26 | 36.7 | 90 | 157.7 | 0.91 | |

0.4L | 2.7 | 2.5 | 20 | 54.3 | 90 | 169.0 | 0.9 | |

0.5L | 9.1 | 8.3 | 16 | 171 | 90 | 294.0 | 0.85 |

Where,

^S = Shrinkage

^C= Creep

^E = Shortening of concrete

^A = Slip in anchorage

^F = Friction

^R = Relaxation

n= Efficiency

**After Losses, effective Prestressing Force**

1. (P) = P (1-Losses) = 14011.51 kN

2. Table.7 Calculation of Stresses at top and bottom fiber

**Compressive Stress at**

1. Transfer = 6.66 < 0.5 fcj = 20 mpa

2. Service = 8.367 < 0.33 fck = 16.5 mpa

**Tensile stress at**

1. Initial Stage = 2.979 < 3mpa (As per IS:1343 – 1980)

2. Working Stage = No tensile stress

### Design of Reinforcement in Box Girder Bridge

P =14011.51 kN, d = 1350 mm, bw = 200 mm

Assume 150 mm wide and 150 mm deep distribution plate, located concentrically at centre.

ypo /y0 = 75/150 = 0.5,

As per IRC:18-2000, From table value of Fbst/ Pk = 0.17 and Fbst = 452.753 kN

Using 12 mm diameter links, area of steel links is,

Ast = 1254 mm/2

Providing 24 bars of 12 mm dia, 750mm also bar of 12 mm dia @ 110 mm c/c horizontally to form

mesh.

### Side Face Reinforcement

As per clause 18.6.3.3 of IS:1343-1980

Ast = 0.05 x 1350 x 300/100 = 202.5 mm/2

Provide 6 – 12 mm dia on each face of web

### Design of Deck Slab

Using M30 grade concrete and Fe415

Total moment due to DL+SIDL+LL = 1427.0 kN.m

Depth required = 150.4 < 250 mm

### Main Reinforcement

Ast = 3192.6824 mm/2

Providing 16mmØ bars dia 100 mm c/c

### Design of Transverse Reinforcement

M = 0.3ML + 0.2(MDL + MSIDL)

M = 324 kN.m

Ast = 724.74 mm/2

Providing 12 mm dia bars @ 160 mm c/c

### (d) Comparsion of Result for Various Span/Depth Ratio

The comparison of prestress force, deflection and stresses values are obtained for various span/depth ratio (table no. 10 & 11) for box girder bridge. The values are calculated as per IS:1343-1980.

Permissible (DL-Prestress Force) = 12 mm

Permissible (DL-LL-Prestress Force) = 85.7 mm