DAVID GUTIERREZ RIVERA

F U N D A M E N TA L S O F

B R I D G E D E S I G NA A S H T O / L R F D

U S C / M K S

1 s t D R A F T

Units Conversion Table

Length

1m = 100 cm 1 ft = 12 in

1m = 3.28 ft 1 cm = 0.3937 in1 ft = 0.305m 1 in = 2.54 cm

Section Properties

1m2 = 10.76 ft2 1 in2 = 6.45 cm2

1m3 = 35.3 ft3 1 in3 = 16.387 cm3

1m4 = 115.743 ft4 1 in4 = 41.623 cm4

Loads

1 kg = 9.81N 1 t = 1000 kg

1 lb = 4.448N 1 t = 2.20 klb1 klb/ft = 14.59 kN/m 1 lb/ft = 1.488 kg/m1klb/ft2 = 47.9 kN/m2 1 lb/ft2 = 4.88 kg/m2

1 klb/in2 = 6.895MPa 1klb/in2 = 70.307 kg/cm2

Moments

1 klb · ft = 1.356 kN ·m 1klb · ft = 138.255 kg ·m1kN ·m = 101.97 kg ·m 1kg ·m = 7.233 lb · ft

Density

1 kN/m3 = 6.3654 lb/ft3 1 lb/ft3 = 16 kg/m3

DAVID GUTIERREZ RIVERA

F U N D A M E N TA L S O F

B R I D G E D E S I G NA A S H T O / L R F D

U S C / M K S

1 s t D R A F T

Copyright © 2016 David GUTIERREZ R IVERA

PUBLISHED BY 1st DRAFT

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First printing, August 2016

To my Family

and students . . .

Contents

1 Basic Concepts 19

2 Materials 31

3 Mechanics of Materials 33

4 Loads on Bridges 35

5 Analysis of Bridges 47

6 Design Philosophy 49

7 Culverts 53

8 Slabs 55

9 Girders 57

10 Trusses 59

11 Integral Bridges 61

12 Abutments 63

13 Piers 65

14 Foundations 67

15 Accessories 69

A Box Culverts Formulas 73

Bibliography 75

Index 77

Symbols

Kg Girder longitudinal stiffness [in4(cm4)]. 42, 43

L Span length [ft(m)]. 42, 43

N Number of girders. 42

de Distance from curb to girder edge [ft(m)]. 44

eg Distance between the centers of gravity of slab and girder [in(cm)]. 43

n Elastic Modulus ratio. 43

s Girder spacing [ft(m)]. 42, 43

ts Slab thickness [in(cm)]. 42, 43

A Area [in2(cm2)]. 43

I Inertia [in4(cm4)]. 43

Acronyms

BR Braking Force. 38

CE Vehicular Centrifugal Force. 38

CT Vehicular Collision Force. 39

DC Dead Load from Structural Components and Attachments. 35, 52

DD Downdrag. 41

DF Distribution Factors. 42

DW Dead Load from Wearing Surface and Utilities. 35, 52

EH Horizontal Earth Load. 39, 52

EL Erection Load. 41, 52

ES Earth Surcharge. 39, 52

EV Vertical Earth Load. 39, 52

Ft Fatigue. 38

HL-93 Highway Load (1993). 36

IM Vehicular Dynamic Load. 38

La Design Lane Load. 38

LL Vehicular Live Load. 36

LRFD Load and Resistance Factor Design. 35, 42, 49, 75

LS Live Load Surcharge. 39

m Multiple Presence Factor. 42

12

PL Pedestrian Live Load. 38

RC Reinforced Concrete. 24

Ta Design Tandem Load. 36

Tr Design Truck Load. 36

List of Figures

1.1 Bridge Superstructure and Substructure. 19

1.2 Typical Bridge Components. 20

1.3 Typical Bridge Section Components. 20

1.4 Typical Bridge Components. 20

1.5 Typical 3-Lane Highway Bridge Cross-Section. 21

1.6 Median Widths for Freeways. From A Policy on Geometric Design of High-

ways and Streets [AASHTO, 2011]. 22

1.7 Horizontal Clearance. From A Policy on Geometric Design of Highways

and Streets [AASHTO, 2011]. 22

1.8 Interstate closure after an impact with a bridge. 22

1.9 Types of Bridges. 23

1.10A Box Culvert in Tegucigalpa, Honduras. 23

1.11A Concrete Girder Bridge, in Tegucigalpa, Honduras. 24

1.12Steel Girders for a Bridge, in Tegucigalpa, Honduras. 24

1.13Typical minimum depths for superstructures. 24

1.14A frame bridge in Tegucigalpa, Honduras. 25

1.15Types of Truss Bridges. 25

1.16Pont du Gard Aqueduct, France. https://en.wikipedia.org/wiki/

Pont_du_Gard 26

1.17Cantilever Bridge Human Model. https://en.wikipedia.org/wiki/

Forth_Bridge 26

1.18Forth Bridge, Scotland. https://en.wikipedia.org/wiki/Forth_Bridge 26

1.19Millau Viaduct, Aveyron, France. https://es.wikipedia.org/wiki/

Viaducto_de_Millau 27

1.20The Akashi-Kaikyo Suspension Bridge, Japan 1998. https://www.youtube.

com/watch?v=N9fbRcRJY34 27

1.21Bridge Design Process. 28

14

4.1 Superstructure Loads 36

4.2 Common Construction Materials Densities. [AASHTO, 2012] 37

4.3 HL-93 Design Truck Load. [AASHTO, 2012] 37

4.4 HL-93 Design Tandem Load. [AASHTO, 2012] 38

4.5 HL-93 Design Lane Load. [AASHTO, 2012] 38

4.6 Horizontal Earth Load (EH). 39

4.7 Horizontal earth pressure conditions. 40

4.8 Active and passive horizontal earth pressures. 40

4.9 Live load distribution for fill depth less than 2 ft (0.6m). 44

4.10Live load distribution for fill depth of 2 ft (0.6m) or greater. 45

4.11Live load distribution overlap for fill depth of 2 ft (0.6m) or greater. 45

List of Tables

1.1 Typical Roadway Widths for Highways. From A Policy on Geometric Design

of Highways and Streets [AASHTO, 2011]. 21

1.2 Vertical Clearance. From A Policy on Geometric Design of Highways and

Streets [AASHTO, 2011]. 22

4.1 Dynamic Load Allowance. [AASHTO, 2012]. 38

4.2 Multiple Presence Factors 42

4.3 Distribution Factors for Interior Girders 43

4.4 Distribution Factors for Exterior Girders 44

6.1 Load Combinations 51

6.2 Load Factors γp 52

6.3 EV Load Factors γp 52

6.4 Concrete Resistance Factors φ 52

6.5 Steel Resistance Factors φ 52

Preface

IN THIS BOOK a dual units system approach has been adopted. Two versions

of the book are available, one in SI/USC and the other in USC/MKS system.

This version of the book is in the USC / MKS system. The MKS system refers

to the non-standard units system known as the Gravitational Metric System.

It is built on the three base quantities length, time and force with base units

meter, second and kilogram-force respectively. This unit system is popular in

Latin-America.

In this edition of the book a focus towards small to medium span bridges has

been adopted. Long span bridges might be covered in a future release.

Comprehensive design examples. . . .

In this book LRFD is adopted.

Acknowledgements

I want to thank . . .

About the Author

1

Basic Concepts

" W H E N T H E H I S T O R Y O F O U R T I M E I S W R I T T E N , P O S T E R I T Y W I L L K N O W U S N O T B Y A

C AT H E D R A L O R T E M P L E , B U T B Y A B R I D G E . "

M O N T G O M E R Y S C H U Y L E R 1 8 7 7 , W R I T I N G A B O U T T H E B R O O K LY N B R I D G E .

1.1 Introduction

Definition, Some history Log Bridge the ”start” ...

1.2 Bridge Components

A bridge can be subdivided into two main components:

• The Superstructure and

• the Substructure

These are illustrated in Fig. 1.1.

Figure 1.1: Bridge Superstructure and Sub-structure.

20 1. BASIC CONCEPTS

A SUPERSTRUCTURE comprises all the elements of a bridge which are above

the supports. These include:

Figure 1.2: Typical Bridge Components.

Wearing Surface. ADD content ...

Deck. ADD content ...

Beams, Stringers or Girders. They are the primary elements which support

the loads from a bridge superstructure and span the longitudinal clearance of

a bridge. They can be made up of Rolled Steel Beams, Steel Plate Girders,

Reinforced or Prestressed Concrete and even Glulam Timber or Aluminum.

Figure 1.3: Typical Bridge Section Compo-nents.

Diaphragms. Diaphragms are structural elements used for lateral bracing and

spread both vertical and horizontal loads to the beams, which in turn transfer

them to the substructure. In curved girder bridges, diaphragms are primary el-

ements, because they are require for load carrying capacity, like torsion caused

from vertical loads.

Railings or Barriers. ADD content ...

Drainage. ADD content ...

Figure 1.4: Typical Bridge Components.

THE SUBSTRUCTURE of a bridge are all the elements required to support the

superstructure. These include:

Abutments. Abutments are earth-retaining structures supporting the bridge

superstructure at the ends of it.

Piers. Piers are structures supporting the superstructure at intermediate points,

thus reducing its span.

Bearings and Joints. Bearings are mechanical devices which directly transfer

vertical and horizontal loads form the superstructure to the substructure. Some

types of bearings are: Steel Rollers which is a type of fixed bearing which

1.3. GEOMETRIC DESIGN 21

allows rotation but prevents translation. Neoprene pads, which are considered

expansion joints, because they allow both rotation and translation. ADD more

about Joints ...

Approach Slab. ADD content ...

1.3 Geometric Design

A BRIDGE GEOMETRIC DESIGN is usually restricted to have the same dimen-

sions as of the approaching highway. For the geometric design of highways re-

fer to A Policy on Geometric Design of Highways and Streets [AASHTO, 2011].

Figure 1.5: Typical 3-Lane Highway BridgeCross-Section.

Roadway

THE ROADWAY WIDTH is comprised of the lane width and the shoulder width.

Lane width influences the comfort of driving and operation. A 12 ft (3.6m) lane

is predominant on most high-speed high-volume highways.

Roadway Width

Lane Width 12 ft (3.6m)Right Shoulder 10 ft (3.0m)Left Shoulder

4 lanes or less 4 ft (1.2m)more than 4 lanes 10 ft (3.0m)

Table 1.1: Typical Roadway Widths for High-ways. From A Policy on Geometric Design ofHighways and Streets [AASHTO, 2011].

Shoulders is the portion of the roadway contiguous to the lane which serves

to accommodate stopped vehicles, for emergency use, or even bicyclists. It

varies in width from only 2 ft (0.6m) on minor rural roads to approximately 12 ft

(3.6m) on major highways.

The clear roadway is the distance between curbs on a roadway. Typical road-

way width values for highways are shown in Table 1.1.

Median

A MEDIAN BARRIER must be provided to separate the traffic for two-way ele-

vated freeways in urban settings. The width of the barrier is of 2 ft (0.6m). The

22 1. BASIC CONCEPTS

minimum median width should be the width of the barrier plus two shoulder

width’s, see Fig. 1.6.

Figure 1.6: Median Widths for Freeways.From A Policy on Geometric Design of High-ways and Streets [AASHTO, 2011].

Clearance

M IN IMUM HORIZONTAL CLEARANCES should be provide to improve visibility

and reduce the sense of restriction for travelers. Theses are usually provided

with the shoulder width, as shown in Fig. 1.7.

Figure 1.7: Horizontal Clearance. From APolicy on Geometric Design of Highways andStreets [AASHTO, 2011].

THE MINIMUM VERTICAL CLEARANCE for freeways and arterial systems is

16 ft (4.9m). For other routes, a lower vertical clearance is acceptable, al-

though it is usual preference to provide 17 ft (5m) of vertical clearance in all

routes were possible. Table 1.2 show the vertical clearance required for differ-

ent types of roadway.

Type of Roadway Height

Freeway and Arterial 16 ft (4.9m)Local and Collector 14 ft (4.3m)

Table 1.2: Vertical Clearance. From A Pol-icy on Geometric Design of Highways andStreets [AASHTO, 2011].

Consequences of inappropriate clearances is illustrated in Fig. 1.8.

ADD content for Skewed Bridges ...

Figure 1.8: Interstate closure after an impactwith a bridge.

1.4 Aesthetics

ADD content Archineering ...

1.5 Bridge Types

BASED ON THEIR FUNCTIONALITY, bridges can be classified as:

• Highway

• Pedestrian

• Aqueduct

• Railroad

1.5. BRIDGE TYPES 23

• Viaduct

• Movable (Drawbridge)

BASED ON THE SPAN LENGTH, bridges can be classified as:

Short-span 20 ft (6m) to 65 ft (20m)

Medium-span 65 ft (20m) to 400 ft (125m)

Long-span over 400 ft (125m)

The following are the most basic types of bridges classified according to their

structural system. This affects both the construction process and the span it is

able to cover. They are sorted on increasing span length capability.

Figure 1.9: Types of Bridges.

Graph of types of bridges distribution in the world, pie chart.

Graph of optimal span for bridge types, and maximums.

Culverts

These common structures work as a frame retaining soil at its sides and sup-

porting traffic loads in the superior and/or inferior slab. They are usually used

for drainage of small streams or one lane traffic overpasses. Their structural

form can be a circular pipe or a rigid frame box. Optimal spans go up to around

20 ft (6m) and the usual span-to-depth ratio for the slab is of 15.

Figure 1.10: A Box Culvert in Tegucigalpa,Honduras.

Buried structures with spans less than 10 ft (3m) are not considered bridges.

Usually these small buried structures don’t require extensive analysis and are

selected from standard designs. Buried structures with longer spans are con-

sidered bridges and require bridge analysis and design. The design of a box-

culvert is discussed in Section 6.6.

24 1. BASIC CONCEPTS

Slab Bridges

These consist on a slab covering a span in an unidirectional way. They are

usually used for one lane traffic overpasses. Their optimal spans go up to

around 30 ft (10m). The usual span-to-depth ratio for the slab is of 20.

Girder Bridges

Optimal spans range from 30 ft (10m) to 500 ft (150m), depending on the

material and type of construction. Usual span-to-depth ratios for girders are 18

for concrete and 25 for steel. Usual girder spacing range from 8 ft (2.4m) to

10 ft (3.0m)

Figure 1.11: A Concrete Girder Bridge, inTegucigalpa, Honduras.

For short spans, from 30 ft (10m) to 60 ft (20m), Reinforced Concrete (RC)

T-Beams are generally an economical choice, while Rolled wide-flange Steel

Beams are economical for spans up to 100 ft (30m). Usual span-to-depth ratio

is of 15 for RC T-Beams and 25 for Steel Beams. It is usually preferable to have

composite action in steel girder bridges because of the more efficient design.

Usually shear studs are used for this effect. Also cover-plates may be used to

increase flexural resistance in places with high flexural stress. Maintenance and

transportation costs should be analyzed when selecting between a concrete vs.

steel alternative.

Figure 1.12: Steel Girders for a Bridge, inTegucigalpa, Honduras.

For medium spans, from 30 ft (10m) to 150 ft (50m), Prestressed Concrete

Beams and Steel Plate Girders are the most economical choice. With long

girders, transportation of precast members may present an issue, so post-

tensioned, cast-in-place RC boxes or even steel plate girders may be a better

option.

Figure 1.13: Typical minimum depths for su-perstructures.

For longer medium spans, from 60 ft (20m) to 500 ft (150m), Post-tensioned

1.5. BRIDGE TYPES 25

box girders and steel box girders become the most economical choice. Box

girders are also desirable in curved alignments because of their high torsional

resistance.

Research ...

Construction Types analysis and design examples. Bay by Bay, Cantilever Method,

Incremental Launching. ”Segmental Construction.” References: Podolny and

Muller (1982) and ASBI (2003).

Integral Bridges

They can also be known as Frame or Portal Bridges. Optimal spans range from

150 ft (50m) to 650 ft (200m). Record max. is of 820 ft (250m).

This bridges are built with neither expansion joints or bearings. Therefore they

are subject to considerable thermal loading, which has to be carried by the

integral bridge. Research has shown that these bridges have trouble in the

geotechnical aspects.

Figure 1.14: A frame bridge in Tegucigalpa,Honduras.

References: Cheng(1960), White (1976), Heins and Firmage (1979) PCA (1966).

Truss Bridges

Optimal spans ranges from 300 ft (100m) to 1000 ft (300m). Record maximum

built is of 1500 ft (450m).

Figure 1.15: Types of Truss Bridges.

They are usually made of steel members, although they can also be made

of timber. It is usually preferred to have some redundant members for safety.

Although determinate trusses are cheaper, many trusses have failed when a

26 1. BASIC CONCEPTS

member is overloaded. Having no redundant members, complete collapse of

the structure have occurred.

References: Cooper (1889), Waddell (1916), Shedd (1972).

Figure 1.16: Pont du Gard Aqueduct,France. https://en.wikipedia.org/

wiki/Pont_du_Gard

Arch Bridges

The oldest types of bridges ever built, an example is shown in Fig. 1.16.

Arched or haunched Concrete and steel girders optimal spans range from 400 ft

(125m) to 1000 ft (300m).

Arched Steel Trusses can span even longer than simple trusses. They are

usually optimal for spans from 300 ft (100m) to 1800 ft (550m).

References: Xanthakos and Troitsky (1994).

Cantilever Bridges

Figure 1.17: Cantilever Bridge HumanModel. https://en.wikipedia.org/

wiki/Forth_Bridge

This types of bridges are those constructed using the balanced cantilever method

of construction. The basic principles of this design where demonstrated by Sir

Benjamin Baker, with the ”Human Cantilever” shown in Fig. 1.17.

A typical example is the Scottish Forth Bridge shown in Fig. 1.18.

Figure 1.18: Forth Bridge, Scotland.https://en.wikipedia.org/wiki/

Forth_Bridge

Optimal spans range from 800 ft (250m) to 1800 ft (550m).

Cable-stayed Bridges

Theses type of bridges might be the most innovative types of bridges from

the last century. Economically they are very competitive for medium and long

1.6. PROJECT INCEPTION 27

span bridges, with usual optimal spans oscillating from 650 ft (200m) to 2000 ft

(600m), although maximums of 3300 ft (1000m) have been built.

Construction of such bridges pretty much follows the same principles of the

balanced cantilever method. Construction starts at the pylons while hanging

from them the inclined cables or stays. Explain construction methods

Figure 1.19: Millau Viaduct, Aveyron,France. https://es.wikipedia.org/

wiki/Viaducto_de_Millau

References: O’Connor (1977), Kavanagh (1972), Podolny and Scalzi (1986),

Troitsky (1988), Heins and Firmage (1979), Smith (1967), Tang (1971), Lazer

(1972), Simpson (1970), Thul (1966, 1972), Demers and Simonsen (1971),

Narouka (1973), Stahl and Christopher (1992), Leonhardt (1987)

Suspension Bridges

These are the types of bridges for covering the longest spans. They become

optimal for spans of 1500 ft (500m). Currently the longest suspension bridge

is the Akashi-Kaikyo Suspension Bridge, shown in Fig. 1.20 with a main span

of 6530 ft (1991m).

Figure 1.20: The Akashi-Kaikyo Suspen-sion Bridge, Japan 1998. https://www.

youtube.com/watch?v=N9fbRcRJY34

1.6 Project Inception

ADD content, Surveying Location ...

1.7 Construction Methods

Balanced Cantilever

28 1. BASIC CONCEPTS

Figure 1.21: Bridge Design Process.

1.8. MAINTENANCE AND REHABILITATION 29

Segmental

ADD content ...

1.8 Maintenance and Rehabilitation

1.9 Vocabulary??

1.10 Historical Background

Bridge Failures

2

Materials

2.1 Concrete

ADD Design Aids for Reinforced Concrete, Prestressed Concrete, Masonry

2.2 Steel

ADD tables for Hot Rolled Laminated Beams, Plate Girders

2.3 Timber

ADD content ...

3

Mechanics of Materials

3.1 Section Properties

ADD content ...Moment of Inertia, Section Modulus , Centroids etc.

Tables for common Steel sections properties.

3.2 Axial Loading

Tension and Compression. ADD content ...

3.3 Bending

Flexure and Shear. ADD content ...

3.4 Buckling

ADD content ...

3.5 Torsion

ADD content ...

3.6 Plasticity

ADD content ...

34 3. MECHANICS OF MATERIALS

3.7 Other Topics

ADD content ... Thermal Expansion, Fatigue, Creep, etc.

4

Loads on Bridges

" C A R G A S . "

C A R G A D O .

IN THIS CHAPTER we’ll introduce the different types of loads affecting a bridge.

Loads are classified according to the Load and Resistance Factor Design (LRFD)

Bridge Design Specifications [AASHTO, 2012] with their corresponding acronyms.

ACTIONS IN A BRIDGE may be classified as:

• Gravity Loads

• Lateral Loads

• Longitudinal Loads

These can be either Permanent or Transient.

4.1 Dead Loads (D)

DEAD LOADS are a type of permanent load that usually comes from materi-

als self-weight. A table with the most common construction materials used in

bridges and their densities is shown in Fig. 4.2.

Superimposed Dead Loads are those loads which are placed in a structure

after it has cured. These loads are separated from the other loads because

they are resisted by a stronger section with composite action.

Two main types of dead loads exist:

DEAD LOAD FROM STRUCTURAL COMPONENTS AND ATTACHMENTS (DC)

refers to structural components self-weight, like beams, decks and diaphragms,

which are part of the structural system. Attachments like railings, curbs and

others are also considered in this category.

DEAD LOAD FROM WEARING SURFACE AND UTIL IT IES (DW) refers to the

36 4. LOADS ON BRIDGES

Superstructure Loads

Gravity Loads

Dead Load (D)

StructuralComponents

(DC)

Wearing Surfaceand Utilities (DW)

Live Load (L)

Vehicular (LL)

Truck (Tr) Tandem (Ta) Lane (La)

Impact (IM)

Fatigue (Ft)

Longitudinal Loads

Braking Force (BR)

Thermal (TH)

Lateral Loads Earthquake (EQ)

Wind (WL)

CentrifugalForce (CE)

Figure 4.1: Superstructure Loads

wearing surface used in the superstructure for traffic, which are subject to wear.

4.2 Live Loads (L)

L IVE LOADS on a bridge are those which move along the span through time.

These are the transient type of load.

VEHICULAR L IVE LOAD (LL) on a bridge are modeled by using the Highway

Load (1993) (HL-93). This model is composed by a set of three different live

loads configurations, which are:

• THE DESIGN TRUCK LOAD (TR), shown in Fig. 4.3, consists of three axle

loads. The front axle is of 8 klb (3.64 t), followed by the drive axle of 32 klb

(14.55 t) at 14 ft (4.27m), and the rear axle also of 32 klb (14.55 t) located

at a variable position from 14 ft (4.27m) to 30 ft (9.1m), which ever causes

the maximum load effects. A dynamic allowance needs to be considered for

this type of load, see Section 4.2.

• THE DESIGN TANDEM LOAD (TA) (Ta), shown in Fig. 4.4, consists of two

axle loads. Both axles have a load of 25 klb (11.36 t) and are separated 4 ft

(1.22m). A dynamic allowance should be considered, see Section 4.2.

4.2. LIVE LOADS (L) 37

Figure 4.2: Common Construction MaterialsDensities. [AASHTO, 2012]

Figure 4.3: HL-93 Design Truck Load.[AASHTO, 2012]

38 4. LOADS ON BRIDGES

Figure 4.4: HL-93 Design Tandem Load.[AASHTO, 2012]

• THE DESIGN LANE LOAD (LA), shown in Fig. 4.5, consists of a uniformly

distributed load of 0.64 klb/ft (0.95 t/m), no dynamic allowance is neces-

sary. THE DESIGN LANE WIDTH may or may not be the same as the traffic

lane width from Section 1.3. AASHTO uses a width of 10 ft (3.05m) for the

design lane. The number of design lanes is taken as the integer of the ratio

of the clear roadway width divided by 12 ft (3.66m).

Figure 4.5: HL-93 Design Lane Load.[AASHTO, 2012]

The overall effect of the vehicular live loads consists of a combination of these

loads. The load effects of the design truck and the design tandem must each be

superimposed with the load effects of the design lane load. We emphasize that

these loads are not for any particular vehicle or combination of vehicles, they

are rather representative of the overall vehicular live loads and their associated

load effects.

Truck Wheels are spaced transversely at 6 ft (1.8m).

Tire Contact Area for vehicular live loads is considered to be a rectangle with

a width of 20 in (50 cm) and a length of 10 in (25 cm).

Some effects of vehicular live loads on bridges are:

• DYNAMIC LOAD (VEHICULAR DYNAMIC LOAD ( IM)) , also commonly

known as Vehicular Dynamic Load (IM), is a magnification to the static loads

from the axles of a vehicle. These magnification are caused by oscillation of

the axles when passing through the rough surface of the roadway.

Impact is represented by percentage increase of the static load, know as

Dynamic Allowance. Theses are shown in Table 4.1, for different bridge

components and Limit States. Typically a 33% increase is adopted for most

cases.

Component IM(%)

Deck Joints 75All other ComponentsFatigue and Fracture Limit States 15All other Limit States 33

Table 4.1: Dynamic Load Allowance.[AASHTO, 2012].

• FATIGUE (FT) is present in bridge structural components because they are

subject to cyclic loading from vehicular live loads. For checking the Fatigue

Limit State a Fatigue Truck is used. This is the same as the Design Truck

from Fig. 4.3, with the only exception that the variable axle is set to a con-

stant value of 30 ft (9.1m).

• BRAKING FORCE (BR) are longitudinal forces caused by braking of vehic-

ular live loads. Add more ...

• VEHICULAR CENTRIFUGAL FORCE (CE) are lateral loads that can occur

in horizontally curved bridges. Add more ...

OTHER LIVE LOADS on bridges are:

• PEDESTRIAN L IVE LOAD (PL): a usual pedestrian load of 75 lb/ft2 (366 kg/m2)

is applied simultaneously with the vehicular live loads. Add more ...

4.3. EARTH LOADS (E) 39

• Deck and Railing Load Add ...

• Special Vehicles, Train Loads Add ...

• VEHICULAR COLLISION FORCE (CT) Add ...

4.3 Earth Loads (E)

EARTH LOADS are considered a type of permanent load . They can be classi-

fied into three types:

• VERTICAL EARTH LOAD (EV) are loads caused by soil self-weight. Usual

values of soil specific weight are around 100 lb/ft3 (1600 kg/m3) to 120 lb/ft3

(1900 kg/m3). These loads must me considered for buried structures like

culverts. Soil-structure interaction may apply. They also serve as stabilizing

loads in abutments and wingwalls . Add soil-structure interaction factor (Fe)

...

• SURCHARGE LOADS are caused by additional loads over an earth fill. These

are separated into Earth Surcharge (ES) of the permanent type and Live

Load Surcharge (LS) of the transient type. Add Boussinesq theory of load

distribution...

• HORIZONTAL EARTH LOAD (EH) are lateral loads affecting retaining struc-

tures, like abutments and wing walls, which cause overturning and sliding

effects on the structure. These loads are a function of the geo-technical

properties of soil.

A fluid-like pressure model is usually used to model horizontal earth loads.

This way earth pressure is given by:

Ps = ksγsh (4.1)

Figure 4.6: Horizontal Earth Load (EH).

This load has a triangular distribution increasing with depth, with a resultant

of P = 12 ksγsh2 located at 1

3 h from the base, as shown in Fig. 4.8.

Types of horizontal earth pressure are active, passive and at-rest condition.

These are illustrated in Fig. 4.7. Each of these is assigned a coefficient of

earth pressure (ks).

For the at-rest condition (k0), the earth pressure coefficient is:

k0 = 1− sin φ (4.2)

40 4. LOADS ON BRIDGES

Figure 4.7: Horizontal earth pressure condi-tions.

At-rest soil pressure conditions occur when there is no horizontal displace-

ment of the retaining soil. This is usually the case for buried structures like

culverts.

One of the most complete and analytical theories for horizontal earth pres-

sures is Coulomb’s Theory and is widely used for bridge design. Active and

passive earth pressures are illustrated on Fig. 4.8. The equations for the

active and passive earth pressure coefficients are as follow:

Figure 4.8: Active and passive horizontalearth pressures.

For the active case (ka),

ka =cos2 (φ− θ)

cos2 θ cos (δ + θ)

(1 +

√sin (δ+φ) sin (φ−α)cos (δ+φ) cos (θ−α)

)2 (4.3)

Active pressure case is the one causing horizontal displacement on a wall.

For the passive case (kp),

kp =cos2 (φ + θ)

cos2 θ cos (δ− θ)

(1−

√sin (φ−δ) sin (φ+α)cos (δ−θ) cos (α−θ)

)2 (4.4)

Passive pressure case is the one resisting horizontal displacement on a wall.

4.4 Earhtquake Loads (EQ)

ADD Simulations, Experiments, Momonobe-Okabe theory of seismic earth pres-

sure.

4.5 Fluid Loads ()

4.6. MISCELLANEOUS LOADS 41

Water Loads (WA)

ADD Static case, Stream Loads, Flood Loads ...

Wind Loads

ADD Drag Coefficient.

W IND LOADS ON STRUCTURE (WS)

W IND LOADS ON L IVE LOAD (WL)

Simulations (CFD), Experiments ...

4.6 Miscellaneous Loads

Downdrag (DD) Erection Load (EL) ADD content ...

Construction Loads.

Accidental, ... Debri collisions in streams ...

Creep and Shrinkage

Ice Loads (IC)

Snow Loads

Settlement (SE)

Uplift

Friction Effects (FR)

ADD content ...

Thermal Effects (TH)

ADD content ...

Blast and Collision

ADD content Vessel Collision, Extreme Event (EX) ...

42 4. LOADS ON BRIDGES

4.7 Live Loads Distribution

LOADINGS IN A BRIDGE are distributed among elements of the bridge pass-

ing from the superstructure to the substructure. The following are the main

concepts influencing the distribution of loads on a bridge.

Multiple Presence

Because it is possible to have more than one lane simultaneously loaded,

AASHTO has provided the use of a Multiple Presence Factor (m) to account

for this effect. The normal case is taken to have two lanes loaded simultane-

ously, so the factor is taken as one for this case.

Design Lanes m

1 1.202 1.003 0.85

4 or more 0.65

Table 4.2: Multiple Presence FactorsLateral Distribution

G IRDER BRIDGES have live loads distributed transversely to each girder. Some

girders take most of the load depending on the position of the live load on the

section of the bridge. The amount of load distributed to a girder is affected by

several factors some of which are:

• Type and depth of deck

• Span length

• Girders spacing and stiffness

• Diaphragms spacing and stiffness

• Type of bracing

• Loads

• Horizontal alignment (curved or straight)

Considering these factors [AASHTO, 2012] LRFD Bridge Design Specifications

has provided Distribution Factors (DF) for moments and shears.

REQUIREMENTS

To apply these distribution factors it is required to satisfy the following:

• Number of girders (N) ≥ 4

• 3.5 ft(1m) ≤ s ≤ 16 ft(4.85m)

• 4.5 in(11.25 cm) ≤ ts ≤ 12 in(30 cm)

• 20 ft(6m) ≤ L ≤ 240 ft(73m)

• 10× 103 in4(4× 105 cm4) ≤ Kg ≤ 7× 106 in4(3× 108 cm4)

FOR INTERIOR G IRDERS the distribution factors are shown in Table 4.3

4.7. LIVE LOADS DISTRIBUTION 43

Table 4.3: Distribution Factors for InteriorGirders

USC MKS

Mom

ents

SingleLaneLoaded

DFsiM = 0.06 +

( s14

)0.4 ( sL

)0.3(

Kg

12Lts3

)0.1DFsi

M = 0.06 +( s

4.3

)0.4 ( sL

)0.3(

Kg

12Lts3

)0.1(4.5)

MultipleLanesLoaded

DFmiM = 0.075 +

( s9.5

)0.6 ( sL

)0.2(

Kg

12Lts3

)0.1DFmi

M = 0.075 +( s

2.9

)0.6 ( sL

)0.2(

Kg

12Lts3

)0.1(4.6)

She

ars

SingleLaneLoaded

DFsiV = 0.36 +

s25

DFsiV = 0.36 +

s7.6

(4.7)

MultipleLanesLoaded

DFmiV = 0.2 +

s12−( s

35

)2DFmi

V = 0.2 +s

3.6−( s

10.7

)2(4.8)

FOR EXTERIOR G IRDERS with one design lane loaded the lever rule is used.

A truck wheel is positioned at 2 ft (0.6m) from the parapet. The shear and

moments are calculated from the reaction on the exterior girder. With multi-

ple design lanes loaded, moments and shear are calculated using the same

equations for interior girders modified by a correction factor e, see Table 4.4.

Where

Kg = n(

I + Aeg2)

ADD sketch for Lever Arm rule

ADD Skew correction, Transverse Members ...

SLAB BRIDGES D ISTRIBUTIONS ...

BOX BEAMS ...

Buried Distribution

Live loads are spread through soil on buried structures. The general adoption of

design code is to have a linearly varying with depth increase of the contact area

of the wheels conforming the live loads. Two cases of fill height are considered

for the modeling of live load distribution through soil on buried structures.

FIX Figures

CASE Ds < 2′

CASE Ds ≥ 2′

44 4. LOADS ON BRIDGES

USC MKS

Mom

ents

SingleLaneLoaded

Use lever arm rule

MultipleLanesLoaded

DFmeM = eDFmi

M

e = 0.77 +de

9.1

DFmeM = eDFmi

M

e = 0.77 +de

2.8

(4.9)

She

ars

SingleLaneLoaded

Use lever arm rule

MultipleLanesLoaded

DFmeV = eDFmi

V

e = 0.6 +de

10

DFmeV = eDFmi

V

e = 0.6 +de

3.0

(4.10)

Table 4.4: Distribution Factors for ExteriorGirders

Figure 4.9: Live load distribution for fill depthless than 2 ft (0.6m).

4.7. LIVE LOADS DISTRIBUTION 45

Figure 4.10: Live load distribution for fill depthof 2 ft (0.6m) or greater.

OVERLAP

For the HL-93 Live Load overlapping occurs when ... ADD

Figure 4.11: Live load distribution overlap forfill depth of 2 ft (0.6m) or greater.

IMPACT is reduced with the fill’s depth according to the following expression:

IM = 33%(1− 0.125Ds) ≥ 0% (4.11)

5

Analysis of Bridges

5.1 Structural Modeling

Assumptions and Idealizations ...

Models can be:

• Linear

• Planar

• Solids

Linear Elements Types:

• Cable

• Truss

• Frame

Planar Elements Types:

• Shell

• Plate

• Membrane

5.2 Statics

5.3 Deflections

ADD Tables for common Beams Moment, Shear and Deflection Diagrams. ADD

Tables for common Frame Diagrams.

5.4 Structural Analysis

Stiffness Methods

48 5. ANALYSIS OF BRIDGES

Energy Methods

5.5 Influence Functions

ADD content ... Qualitative Influence Lines... Beams, Trusses.

5.6 Dynamics

5.7 Software

6

Design Philosophy

ADD Concepts of Ultimate Limit State (ULS)

ADD Concepts of Serviceability Limit State (SLS), Fatigue, Deflection, Crack

Widths, Vibrations, Drift

ADD Concepts of Extreme Event (EX), Earthquake, Collisions ... ADD content

of Statistical basis

6.1 Load and Resistance Factor Design (LRFD)

The main formula for the LRFD design philosophy is:

φRn ≥∑ ηψiQi (6.1)

Load Multiplier η Section 6.1 Explain ... Importance, Ductility, Redundancy.

STRENGTH I — BASIC LOAD COMBINATION. Load combination related to

normal vehicular use without wind.

STRENGTH I I — SPECIAL VEHICLES. Load combination to be used for spe-

cial vehicles. This load can be assumed acting alone if traffic is restricted in the

event, otherwise combined loads should be used.

STRENGTH I I I — MAXIMUM W IND. Load combination relating to the bridge

being expose to winds exceeding 55mi/h (90 km/h). No live load is consid-

ered in such an event. Similar to the Extreme Events Load Combinations.

STRENGTH IV — H IGH DEAD TO L IVE LOAD RATIO. This load combination

affects mostly bridges with long spans or during construction stages.

STRENGTH V — NORMAL W IND. This load combination relates to normal

vehicular use with a wind of 55mi/h (90 km/h).

EXTREME EVENT I — EARTHQUAKE EVENT. This load combination relates

to earthquake loading. Live load is usually reduce because of the low probability

of both events occurring simultaneously. For normal bridges a value of γEQ =

0.5 is usually used.

50 6. DESIGN PHILOSOPHY

EXTREME EVENT I I — OTHER EXTREME EVENTS. This load combination

is for other extreme events other than earthquake, like collisions, ice loads and

floods to name a few. Only a reduced live load needs to be considered.

SERVICE I — NORMAL USE WITH NORMAL WIND. This load combination

refers to normal operation of the bridge with a normal wind of 55mi/h (90 km/h).

Used for deflection and crack control.

SERVICE I I — STEEL YIELDING. This load combination is for preventing

yielding of steel due to vehicular live load. An average increase of the live

load is used.

SERVICE I I I — TENSION IN PRESTRESSED CONCRETE SUPERSTRUCTURE.

Used for crack control in prestressed concrete superstructures.

SERVICE IV — TENSION IN PRESTRESSED CONCRETE SUBSTRUCTURE.

Used for crack control in prestressed concrete substructures.

FATIGUE I — FATIGUE FOR INFINITE L IFE. Fatigue and fracture load combi-

nation for infinite design life.

FATIGUE I I — FATIGUE FOR F IN ITE L IFE. Fatigue and fracture load combi-

nation for finite design life.

Load Factors and Combinations

6.1. LOAD AND RESISTANCE FACTOR DESIGN (LRFD) 51

Load

sU

seon

eof

thes

eat

atim

e

Load

Com

bina

tion

Lim

itSt

ate

DC

DW DD

EH

EV

ES EL

PS

SH

CR

LL IM CE

BR PL

LSW

AW

SW

LFR

TUTG

SE

EQ

BL

ICC

TC

VSt

reng

thI

γp

1.75

1.00

——

1.00

0.50

/1.20

γT

Gγ

SE—

——

——

Stre

ngth

IIγ

p1

.35

1.00

——

1.00

0.50

/1.20

γT

Gγ

SE—

——

——

Stre

ngth

III

γp

—1

.00

1.40

—1

.00

0.50

/1.20

γT

Gγ

SE—

——

——

Stre

ngth

IV(D

C,

DW

,EH

,EV

&E

S)

γp

—1

.00

——

1.00

0.50

/1.20

——

——

——

—

Stre

ngth

Vγ

p1

.35

1.00

0.40

1.00

1.00

0.50

/1.20

γT

Gγ

SE—

——

——

Extr

eme

Even

tI

γp

γE

Q1

.00

——

1.00

——

—1

.00

——

——

Extr

eme

Even

tII

γp

0.5

1.00

——

1.00

——

——

1.00

1.00

1.00

1.00

Serv

ice

I1

.00

1.00

1.00

0.30

1.00

1.00

1.00

/1.20

γT

Gγ

SE—

——

——

Serv

ice

II1

.00

1.30

1.00

——

1.00

1.00

/1.20

——

——

——

—Se

rvic

eII

I1

.00

0.80

1.00

——

1.00

1.00

/1.20

γT

Gγ

SE—

——

——

Serv

ice

IV1

.00

—1

.00

0.70

—1

.00

1.00

/1.20

—1

.00

——

——

—Fa

tigu

eI

(LL,

IM&

CE

)—

1.50

——

——

——

——

——

——

Fati

gue

II(L

L,IM

&C

E)

—0

.75

——

——

——

——

——

——

Tabl

e6.

1:Lo

adC

ombi

natio

ns

52 6. DESIGN PHILOSOPHY

Load FactorType of Load Max. Min.DC 1.25 0.90DC (Strength IV only) 1.50 0.90DW 1.50 0.65EH (Active) 1.50 0.90EH (At-Rest) 1.35 0.90EV see Table 6.3ES 1.50 0.75EL 1.00 1.00

Table 6.2: Load Factors γp

Load FactorCondition Max. Min.Overall Stability 1.00 N/ARetaining Walls and Abut-ments

1.35 1.00

Rigid Buried Structures 1.30 0.90Rigid Frames 1.35 0.90Flexible Buried Structures• Metal box culverts 1.50 0.90• Thermoplastic culverts 1.30 0.90• All others 1.95 0.90

Table 6.3: EV Load Factors γp

Resistance Factors

Strength Limit State φ

Flexure and Tension• Reinforced Concrete 0.90• Prestressed Concrete 1.00

Shear and Torsion• Normalweight Concrete 0.80• Lightweight Concrete 0.65

Axial Compression 0.75

Bearing 0.70

Compression in Anchorages• Normalweight Concrete 0.80• Lightweight Concrete 0.65

Compression (Strut-and-Tie) 0.70

Table 6.4: Concrete Resistance Factors φ

Strength Limit State φ

Flexure 1.00

Shear 1.00

Tension• Yielding 0.95• Fracture 0.80

Axial Compression• Steel 0.90• Composite 0.90

Shear Connectors 0.85

Table 6.5: Steel Resistance Factors φ

For the extreme limit state the resistance factors φ should be taken as unity.

This is because at this limit state we check for survivability of the structure to

the extreme event. Repairs can be made to the structure when damage has

occurred. This is the most reasonably economical approach.

6.2 Construction & Design Codes

explain AASHTO, ACI, LRFD, CHOC, Difference btw.

7

Culverts

B O X I N

A B O X

ADD content ...

8

Slabs

ADD content ...

8.1 Slab Bridge

8.2 Bridge Deck

9

Girders

9.1 ’L=15m’ Girders

ADD ... RC "T"-Beams and Rolled wide-flange Steel Beams

9.2 ’L=20m’ Girders

ADD Pretensioned concrete beam

9.3 ’L=30m’ Girders

post-tensioned concrete beams and steel plate girder

10

Trusses

10.1 Overview

ADD content ...

10.2 A typical pedestrian truss bridge: the ”Pratt” truss

Loads

Structural Analysis

Steel Design

Timber Design

10.3 A typical vehicular truss bridge: the ”Warren” truss

Loads

Structural Analysis

Steel Design

Timber Design

11

Integral Bridges

11.1 Frames

ADD content ...

12

Abutments

12.1 Parts

ADD content ... Pedestal, Stem, Backwall, Wingwall, Footing: Talon and Feet?

12.2 Cantilever Wall

12.3 Semi-gravity Wall

12.4 Counter-fort Wall

13

Piers

ADD content ...

13.1 Hammerhead

13.2 Column-bent

14

Foundations

ADD content ...

14.1 Piles

15

Accessories

ADD content ...

15.1 Diaphragms

15.2 Bearings and Joints

15.3 Railings, Curbs and Barriers

15.4 Approach Slabs

Approach slabs reduce live load surcharge.

Design Aids

Box Culverts FormulasH

I2

I2

L

I1 I1

A B

CD

k =I2HI1L

y Positive

x Negative

For q 6= w

Ma = Mb = − L2

12· w(2k + 3)− qk

k2 + 4k + 3

Mc = Md = − L2

12· q(2k + 3)− wk

k2 + 4k + 3

For q = w

Ma = Mb = Mc = Md = −wL2

12· k + 3

k2 + 4k + 3

M1 =wL2

8− Ma + Mb

2, M2 =

qL2

8− Mc + Md

2

Ma = Mb = −PL2

24· 4k + 9)

k2 + 4k + 3

Mc = Md = −PL2

24· 4k + 9

k2 + 4k + 3

For k = 1

Ma = Mb = −13PL192

Mc = Md = −7PL192

Ma = Mb = Mc = Md = − pH2k12(k + 1)

For k = 1 and H = L

Ma = Mb = Mc = Md = − pH2

24

M0 =pH2

8− Ma + Md

2

Ma = Mb = − pH2k(2k + 7)60(k2 + 4k + 3)

Mc = Md = − pH2k(3k + 8)60(k2 + 4k + 3)

For k = 1 and H = L

Ma = Mb = −3pH2

160, Mc = Md = −11pH2

480

M0 = 0.064pH2 − (Ma + 0.577(Md −Ma))

Ma = Mb = − (A + D)(2k + 3)− D(3k + 3)3(k2 + 4k + 3)

Mc = Md = −D(3k + 3)− (A + D)k3(k2 + 4k + 3)

A =pb2k60H2 (10H2 − 3b2)

D =pbak2H2

(H2 − a2 − b2 45a− 2b

270a

)

Bibliography

AASHTO. A Policy on Geometric Design of Highways and Streets. American

Association of State Highway and Transportation Officials, 2011.

AASHTO. LRFD Bridge Design Specifications. American Association of State

Highway and Transportation Officials, 2012.

Index

abutments, 20, 39approach slab, 21arch bridges, 26

barriers, 20beams, 20bearings, 20braking force, 38bridge types, 22

cable-stayed bridges, 26cantilever bridges, 26centrifugal force, 38clear roadway, 21culverts, 23, 39

dead loads, 35deck, 20diaphragms, 20distribution factors, 42drainage, 20dynamic allowance, 38dynamic load, 38

earth loads, 39earth surcharge, 39

fatigue, 38

girder bridges, 24girders, 20

HL-93 design lane, 38HL-93 design tandem, 36HL-93 design truck, 36HL-93 fatigue truck, 38horizontal clearance, 22

impact, 38integral bridges, 25

joints, 20

lane width, 21license, 4live load surcharge, 39live loads, 36LRFD, 49

median, 21

neoprene pads, 21

pedestrian live load, 38permanent load, 35, 39piers, 20

railings, 20roadway width, 21

shoulder width, 21slab bridges, 24steel rollers, 20stringers, 20substructure, 19, 20superimposed dead loads, 35superstructure, 19, 20surcharge, 39suspension bridges, 27

truss bridges, 25

vehicular live loads, 36, 38vertical clearance, 22

wearing surface, 20wing walls, 39wingwalls, 39