Bridge Design

Structural Engineering Final Year

History of Bridge Development

• Bridge is one of the oldest instrument of our Civilization.

• In pre-historic times bridge formed with fallen trees or logs of wood

• Suspension Bridges with creepers of tree

• Oldest bridge in record is built on river Niles in about 2650 B.C but no details are available

History

• A wooden bridge built by the queen of Babylon in the year 783 B.C. This bridge has wooden platform supported on stone piers

• Alexander while returning from India used a boat bridge in 326 BC

• Primitive Arch bridge was built in Persia, Greece and Rome

• Oldest Existing Bridge in 350 B.C consist of 20 arches each of 7.5 m span total length is 380 m in Babylon

X-istics of ancient Bridges

1. Crossing to the Right-Angle to the Stream

2. Hump in the Center3. Narrow Width4. Absence of Foot-Path5. Aesthetics

Evolution of Bridge Engineering

• Resulting Combination of the evolution of– Structures –Materials of Construction–Method of Design–Method of Fabrication

• Timber & Stone replaced by –Wrought Iron ----- Mild Steel -----

Concrete----- Pre-stressed------ Suspension bridges---

Span Range Type Material Span Range (m)

Slab Concrete 0-12

Beam ConcreteSteel

12-21030-300

Truss Steel 90-550

Arch Rib ConcreteSteel

90-130120-370

Arch Truss Steel 240-520

Cable ConcreteSteel

90-27090-350

Suspension Steel 300-1400

Components of a Bridge

1. Super Structure– Structural members, beams,

girders, handrails, flooring, arches, cables.

2. Sub Structure– Abutments– Piers– Wing Walls– Foundations for Piers &

Abutments

Basic Definitions

• Bridge– A structure facilitating a

communication route for carrying road, railway, pedestrian traffic or other moving loads over a depression

• Causeway– It’s a pucca submersible bridge

which allows flood water to pass over it. It is provided on less important routes in order to reduce the construction cost of cross drainage structures

Definitions

• Foot Bridge–Bridge Exclusively used for carrying

pedestrians, cycles & animals• Culvert–When a Small stream crosses a road

with linear water way less than 6 meters

• Deck Bridge–Bridges whose floorings are

supported at top of the super structures

Definitions

• Through Bridge–Whose floorings are supported at

the bottom of the super-structure• Cantilever Bridge–More or less fixed at one end and

free on the other end varying from 8m to 20m

• Square Bridge– Bridges at Right-Angle to the axis

of river• Skew Bridge–Bridges which are not at Right-

Angle

Definitions

• Suspension Bridge–Bridges suspended on cables

anchored at ends• Apron– It’s a layer of concrete,

masonry stone, etc placed like flooring at the entrance or outlet of a culvert to prevent scour

• Curtain Wall– It’s a thin wall used as a

protection against scouring action of a stream

Definitions

• Back Wall– Retaining wall to support soil from

approach road• Wing-wall– Retaining the earth from later dimension

• Floor Slab– Provides the carriage way for the

movement of traffic• Stringers– These are the small beams which

transfer the load from floor slab to floor beams

Definitions

• Floor Beam–Transfer the load from stringer to

main girder• Girder–Carries the load of bridge &

Transfer it to the piers & abutments

• Bearings–These behaves as shock absorbers

and caries thermal stresses

Definitions

• Piers– These are the intermediate supports of a

bridge superstructures • Abutments– These are the end supports of the

superstructure• Effective Span– The C/C distance between any two

adjacent supports• Clear Span– The clear distance between any two

adjacent supports

Definitions

• Free Board–Difference between the highest

flood level and the formation level of road embankments on the approaches

• Headroom–The vertical distance between

the highest point of a vehicle and the lowest point of any protruding member of a bridge

Requirements of an Ideal Bridge

• An ideal bridge meets following requirements to fulfill the three criteria of efficiency, effectiveness and equity

1. It serves the intended function with utmost safety and convenience

2. It is aesthetically sound3. It is economical

Selection of Bridge Site

1. Ground Reconnaissance2. Collection of hydraulic/ground data3. Subsoil Investigation4. Type of Bridge5. Engineering Considerations6. Social Considerations7. Aesthetic Considerations8. Future Requirements9. Design Alternatives10.Strategically needed

Ideal Bridge SiteCharacteristics

1. Geologically Suitable2. The stream at bridge site

should be well defined and as narrow as possible

3. There should be a straight reach of stream at bridge site

4. Site should have firm, permanent, straight and high banks

5. Flow of water at bridge site should be steady regime conditions, it should be free from whirls and cross currents

Ideal Bridge SiteCharacteristics

6. It is feasible to have straight approach roads and square alignment

7. Site providing the adequate vertical height available underneath for navigation

8. There should be no adverse environmental input

9. Construction facilities available10.Time Considerations

Types of Bridges

1. W.r.t Materials of Construction1. R.C.C Bridges2. Pre- Stressed Bridges3. Steel Bridges4. Wooden Bridges5. Hanging Cable Bridges

Types of Bridges

2. W.r.t Construction1. Pre- cast Bridges2. Cast Insitu Bridges

3. W.r.t Load Carrying Conditions1. Compression Bridges (Arch

Type)2. Tension Bridges ( Suspension

Type)3. Flexural bridges ( Deck-Girder

Type)

Types of Bridges

4. W.r.t X-Section Conditions1. Solid Slab Bridge2. Hollow Bridge3. Box- Girder Bridge

5. W.r.t Design Conditions4. Slab Bridge5. Deck- Girder Bridge

Types of Bridges

1. Slab Bridge Slab is Supported by

Abutments & Slab is designed as one-way slab supported at edges. The main reinforcement is parallel to the flow of traffic

2. Deck- Girder Bridge The main reinforcement is

perpendicular to the flow of traffic, slab is supported on girders (interior, exterior)

Slab Bridge

Deck – Girder Bridge

AASHTO Design Conditions

1. Design is based on Elastic- Theory

2. AASHTO Stress limitations1. fc = 0.4 fc/ 2. fs = 0.5 fy

3. Span length 1. C/C distance between

supports2. Clear Span + Slab Thickness

(Which ever is larger)

AASHTO Design Conditions

4. Dead Load1. (h / 12)*150 = Slab Weight

2. Weight of Wearing Surface =15 to 30 psf

3. Self weight of (a) Girder (b) Edge beam

5. Live Load1. HS- 20 Truck2. HS- 15 Truck3. Equivalent Lane Load

HS- Truck Loading

14 /

6 /

16000 lbs16000 lbs4000 lbs

2 /

2 /

14 /

6 /

12000 lbs12000 lbs3000 lbs

2 /

2 /

HS-20 Loading

HS-15 Loading

EquivalentLane Loading

PC

w

PC = 18000 lbs 26000 lbs

W = 640 lbs/ft

For HS-20 Loading

For HS-15 Loading Take 3/4 th

Moment Shear

Loading

• Lane Loading / Standard Truck loading shall be assumed to occupy a width of 10 ft

• These loads shall be placed in 12 ft wide traffic lanes spaced across the entire bridge road way

• A 20 to 24 feet wide road shall have two design lanes each equal to half of width of road way

Loading

• Each 10 feet lane loading or single standard truck shall be considered as a unit, and fractional load lane or fractional trucks shall not be used

• Where maximum stresses are caused in any member by loading any number of traffic lanes simultaneously, following % age of resultant live load stresses shall be used– One or Two lanes 100 %– Three Lanes 90 %– More Than 3 lanes 75 %

AASHTO Design Conditions

6. Impact LoadI = 50 / S+125

* S = Span length

I > 30 % of Live Load

Design ofSlab Bridge

• Design of Slab• Design of Edge Beam

Dead Load Moment = w l 2 / 8 Live Load Moment = HS-20 / HS-15

Live Load Moment = 900 *S for S <= 50’Live Load Moment = 1300*S – 20,000 lb-ft

for S > 50’or

= 16000 / E – wE= Equivalent Lane LoadingE= 4 +0.06 * S <=7’

(S+2)/32 * P20 ft-lb per foot width of slab

(S+2)/32 * P15

for HS-20 P = 16,000 lbs for HS-15 P = 12,000 lbs

Design ofDeck Girder Bridge

Design ofSlab Bridge

• Total Moment =D.L Moment + L.L Moment + Impact Load moment

• M = 1 /2 * fc * kd * bjd• K= n / (n+r)

– n = ES /EC = 29* 106 / 57000 √ fc’

• j =1 – (k /3)• r = fs / fc• Cover = 1.5 “ total• As = M / (fs*j*d)

• Distribution Steel = 100 / √ S % age of main steel• Distribution Steel =220/ √ S % age of main steel

(Deck –Girder Bridge)

Design ofEdge Beam

• Dead Load of edge beam• Dead load moment = wl2 /8• Live Load moment = 0.1 pc*SWhere Pc is wheel load

for HS-20 Pc = 16,000 lbs for HS-15 Pc = 12,000 lbs

Example

• Design a slab bridge having clear span of 15 / a clear width of 26 / . Live load HS-20 Truck & wearing surface load is 30 psf. Concrete strength fc’ = 3,000 psi and fy = 40,000 psi

• Solution– S = 15 ’– Clear width = 26 ‘– Live load = HS-20 – fc’ = 3,000 psi– fy = 40,000 psi – Wearing surface = 30psf

Example

• AASHTO allowable Stresses– fc = 0.4 fc ‘ = 0.4 * 3000 = 1200 psi– fs = 0.5 fy = 0.5 *40,000 =20,000 psi

• Load Calculations– Assuming thickness of slab = 12”– Dead load of slab = (12 / 12 )* 150 = 150 psf– Total Dead load = 150 + 30 = 180 psf– Total Dead load moment = wl2 /8

= 180 (16)2 / 8 = 5760 lb-ft

Example

• Moment Calculations– Live load moment = 900 * S = 900 * 16 =

14400 lb-ft– Impact moment = I = 50 / (S+125)

=50 / (16+125) = 0.3570

So we will use 0.3Impact moment = I = 0.3 Live load moment

= 0.3 * 14400 = 4320 lb-ft

• Total Moment calculation– M = 5760 +14400+4320 = 24480 lb-ft

Example

• Using Elastic Theory– k =n / (n+r) – n = Es/ Ec = 29*106 / 57000√3000 = 9.3– r = fs / fc = 20000/1200 = 16.67– k = n / (n+r) = 0.358– j = 1- (k /3) = 1- 0.358/3 = 0.881– M = ½ fc bkd * jd– 24480*12=1/2* 1200*12*0.358*0.881*d2 – d=11.4”– h=d + Cover +0.5 “ = 11.4 +0.75+0.5 =

12.6”– > 12 “

Example

• Using Elastic Theory– Lets assume h = 14 “– Dead load = (14 / 12 ) * 150 = 175 psf– W.S load = 30 psf– Total Dead Load = 175 + 30 = 205 psf– Total Dead load moment = wl2 /8

= 205 (16)2 / 8 = 6560 lb-ft

– Live load moment = 900 * S = 900 * 16 = 14400 lb-ft

Impact moment = I = 0.3 Live load moment = 0.3 * 14400 =

4320 lb-ft

– M = 6560 +14400+4320 = 25280 lb-ft

Example• Calculation of Steel Area– As = M / (fs*j*d)

= (25280*12)/ (20000*0.881*12.75)d= 14-1.25* =

12.75 *(0.5+0.75)

– As = 1.44 in2

–# 7 @ 5” c/c

• Distribution Steel = 100 / √ S % age of main steel

= 100 / √16 = 25 % of main steel = 0.3375 in2

• # 5 @ 10” c/c

Example

• Design of Edge Beam– Dead load of edge beam = ((24 “ * 24” )/144)*15

= 600 lb/ft– Dead load moment = 600 (16)2 /8 = 19200 lb-

ft– Live load moment = 0.1Pc*S = 0.1 (16000

*16)= 25600 lb-ft

– Total Moment = 19200+25600 = 44800 lb-ft– M= ½ fc bkd*jd44800*12 = ½ *1200-24”*0.357*0.881 d2

– d= 10.9 “

Example

• Calculation of Steel Area– As = M / (fs*j*d)

– As = (44800 *12 )/ (20000 *0.881*12.75)

– As =2.39 in2

– Use 7 # 4 bars

–Draw the Sketches Neatly

Example

• Design a Deck-girder bridge having clear span of 48 / a clear width of 29 / . Live load HS-20 Truck & wearing surface load is 15 psf. Concrete strength fc’ = 3,000 psi and fy = 40,000 psi

• Solution– S = 4’- 4”– Clear width = 29‘– Clear Span = 48’– Live load = HS-20 – fc’ = 3,000 psi– fy = 40,000 psi – Wearing Surface = 15 psf

Load Calculations

Assuming thickness of slab = 6”Dead load of slab = (6 / 12 )* 150 = 75 psfTotal Dead load = 75 + 15 = 90 psfTotal (+ & - )Dead load moment = wl2 /10

= 90 (4.333)2 / 10 = 169 lb-ft

Live load moment = 0.80 {(S+2)/32 }* P20 = 0.80 {(4.33+2)/32 }* 16000 =2530 lb-ft

Impact moment = I = 0.3 Live load moment = 0.3 * 2530 = 760 lb-ft

Total Moment calculationM = 169 +2530+760 = 3459 lb-ft

M = ½ fc bkd * jd3459*12 =1/2*1200*12*0.375*0.875*d2

d = 4.19 in

h = 6.5” with 1” cover below # 6 bars assumed then d=4.37 in

As = M / (fs*j*d) = (3459*12)/ (20000*0.875*4.37) = 0.54 in2

# 6 @ 10” c/cDistribution Steel = 220 / √ S % age of main steel

= 220 / √4.33 = 105%of main steel = 0.56 7in2

5# 5 bars

Design of Interior GirderThe interior girders are T beams with flange width equal c/c of girders, the required stem dimensions governed by either Max. moment or max. shear

Assume bridges seats = 2ft

Effective Span length from center of bearings = 50 ft

Dead load from slab on plf of beam = {(6.5/12*150)+15}*5.5

= 528 plf

Assume Section below slab = 14”x 30” (437 plf )Total dead Load on Beam = 965 plf

Dead load moment = (965 x 502 )/8 = 302,000 lb-ft

The absolute Live load moment will occurs with HS 20 loading on the bridge in the position shown in the figure with distribution loads as specified by AASHTOEach interior girder must support 5.5/5 = 1.10 wheel load per wheel, therefore the load from rear wheel is 16000 x 1.1 = 17,600 lb and that from front wheel is 4000 x 1.1 = 4400 lb.