Inroduction to Bridge Engineering

8/7/2019 Inroduction to Bridge Engineering

1/33

Department of Civil Engineering, N-W.F.P UET, Peshawar Introduction to Bridge Engineering

Prof Dr. Qaisar Ali (http://www.eec.edu.pk) Page 1 of 33

(Superstructure) Bridge Deck

Abutment

(Substructure)

Bearing

Pier (substructure)

Pile cap

Pile

Introduction

To

Bridge Engineering


2/33



1. Introduction:Bridges are important to everyone. But they are not seen or understood in the same

way by everyone, which is what makes their study so fascinating. A single bridge

over a small river will be viewed differently by different people.

Civic leaders see the bridge as link between the neighborhoods and a way toprovide fire and police protection and access to hospitals.

In business community, the bridge is seen as opening up new markets andexpanding commerce.

Everyone is looking at the same bridge, but it produces different emotions and visual

images in each one of them.

Bridges affect people. People use them, and engineers design them and later build and

maintain them. Bridges do not just happen. They must be planned and engineered

before they can be constructed.

2. A bridge is the key element in a transportation system It controls the capacity of the system. It is the highest cost per mile of the system. If the bridge fails, the system fails.Because the bridge is the key element in the transportation system, balance must be

achieved between handling future traffic volume and loads and the cost of a heavier

and wider bridge structure. Strength must always be foremost, but so should measures

to prevent deterioration. The designer of new bridge has control over these

parameters and must take wise decisions so that capacity and cost are in the balance,

and safety is not compromised.

3. Role of bridge engineer:Oftentimes engineers deceive themselves into believing that if they gather enough

information about a bridge site and the traffic loads, the selection of a bridge type for

that situation will be automatic. Furthermore the use of analysis/design software will

complete the job.

Unfortunately, or perhaps fortunately it is not the case.


3/33



A bridge engineer must have three points in mind while working on a bridge project.

Creative and aesthetic, Analytical, Technical and practical,So as to give a realistic evaluation of the possibilities of the construction technique

envisaged and the costs involved. If these three mentalities do not coexist in a single

mind, they must always be present on terms of absolute equality in the group or team

responsible for the design.

4. Aesthetics in bridge design:There are no equations, no compute programs or design specifications that can make

our bridges beautiful.

It is an awareness of beauty on our part.

Aesthetics must be a part of the bridge design program from the beginning. It cannot

be added on at the end to make the bridge look nice. At that time, it is too late. From

the beginning, the engineer must consider aesthetics in selection of spans, depth of

girders, piers abutments, and the relationship of one to another. It is a responsibility

that cannot be delegated. We must demand it of ourselves, because the public

demands it of us.

5. Types of bridges:There are a number of ways in which to classify bridges. Bridges can be classified

according to:

Materials (concrete, steel or wood etc), Usage (pedestrian, highway, or railroad), Span (short, medium, or long), Structural form (slabs, girder, truss, arch, suspension, or cable-stayed).They all seem to contain parts of one another within each other.

It is however suitable to classify bridges according to the location of the main

structural elements relative to the surface on which the user travels, that is, whether

the main structure is below, above, or coincides with the deck line.


4/33



a. Main structure below the deck line:Arched and truss-arched bridges are included in this classification.

Examples are the masonry arch, the concrete arch, the steel-truss arch, the steel deck

truss,figs 1 to 5, the rigid frame, and the inclined leg frame bridges,

With the main structure below the deck line in the shape of an arch, gravity loads are

transmitted to the supports primarily by axial compressive forces. At the supports,

both vertical and horizontal reactions must be resisted. The arch rib can be solid or it

can be a truss of various forms.

Salient features of arch type bridges are:

The arch form is intended to reduce bending moments (and hence tensile stresses)in the superstructure and should be economical in material compared with an

equivalent straight, simply supported girder or truss.

The efficiency is achieved by providing horizontal reactions to the arch rib. Ifthese are external reactions, they can be supplied at reasonable cost only if the site

is suitable. The most suitable site for this form of structure is a valley, with the

arch foundation located on dry rock slopes.

The conventional curved arch rib may have high fabrication and erection costs,although these may be controlled by skilled labor. The arch is predominantly a

compression structure. For example, the open spandrel arch with the rib below thedeck consists of deck, spandrel columns, and arch rib. The last two are

compression members. The design must include accurate estimates of buckling

behavior and should be detailed so as to avoid excessive reductions in allowable

stress. The classic arch form tends to favor concrete as a construction material.

The arch rib is usually shaped to take dead load without bending moments. Thisload is then called the form load. If the form load is large, the live load becomes

essentially a small disturbance applied to a compressed member.

The conventional arch has two moments resisting components-the deck and thearch rib. Undesirable and unanticipated distributions of moment may occur,

particularly in regions where the spandrel columns are short, normally near the

crown of the arch, which may be avoided by careful detailing; for example by

using pin ended columns.


5/33



Figure 1: Masonry arch bridge.

Figure 2: Masonry arch bridge.


6/33



Figure 3: Concrete arch bridge.

Figure 4: Steel truss arch bridge.


7/33



Figure 5: Steel deck truss bridge.

b. Main structure above the deck line:Suspension, cable stayed, and through-truss bridges are included in this category.

Both suspension and cable-stayed bridges are tension structures whose cables are

supported by towers, fig. 6 and 8.

Suspension bridges are constructed with two main cables from which the deck,

usually a stiffened truss is hung by secondary cables. Cable-stayed bridges, fig 7,

have multiple cables that support the deck directly from the tower. Analysis of the

cable forces in a suspension bridge must consider non linear geometry due to large

deflections, while linear elastic analysis is usually sufficient for cable stayed bridges.

Salient features of suspension bridges:

The major element of a stiffened suspension bridge is a flexible cable, shaped andsupported in such a way that it can transfer the major loads to the towers and

anchorages by direct tension.

This cable is commonly constructed from high strength wires.


8/33



The deck is hung from the cable by hangers constructed of high strength wireropes in tension.

This use of high strength steel in tension, primarily in the cables and secondarilyin the hangers, leads to an economical structure, particularly if the self-weight of

the structure becomes significant, as in the case of long spans.

The main cable is stiffened either by a pair of stiffening trusses or by a system ofgirders at deck level:

This stiffening system serves to (a) control aerodynamic movements and (b) limitlocal angle changes in the deck. It may be unnecessary in the cases where the load

is great.

It is the only alternative of spans over 600 m, and it is greatly regarded as

competitive for spans down to 300 m.

Salient features of cable-stayed bridges:

As compared with suspension bridges, the cables are straight rather than curved.As a result, the stiffness is greater.

The cables are anchored to the deck and cause compressive forces in the deck. Compared with the stiffened suspension bridge, the cable-braced bridge tends to

be less efficient in supporting dead load, but more efficient in supporting live

load. As a result is not likely to be economical in the longest spans.

The cables may be arranged in a single plane, at the longitudinal centerline of thedeck.

Aerodynamics instability has not found to be a problem in such structures.Salient features of through bridges, fig 9 & 10:

A bridge truss has two main structural advantages: (1) the primary member forcesare axial loads; (2) the open web system permits the use of a greater overall depth

than for an equivalent solid web girder. Both these factors lead to economy inmaterial and a reduced dead weight. The increased depth also leads to reduced

deflection, that is, a more rigid structure,

Economical for medium spans, Aesthetically pleasing.


9/33



Figure 6: Suspension bridge.

Figure 7: Suspension bridge.


10/33



Figure 8: Cable stayed bridge.

Figure 9: Through Bridge.


11/33



Figure 10: Through Bridge

c. Main structure coinciding with the deck line: Girder bridges of all types areincluded in this category.

Examples are:

Slab (solid and voided), T-beam, I-beam, Wide-flange beam, Concrete box girder, Steel box, Steel plate girder.


12/33



Figure 11: Box Girder Bridge.

Figure 12: Girder Bridge under construction.


13/33



Figure 13: Girder Bridge.

6. General Design Considerations:A general statement for assuring safety in engineering design is that the resistance of

the materials and cross section supplied exceed the demands put on them by applied

loads, that is,

Resistance Effect of loads

When applying this simple principle, it is essential that both sides of the inequality be

evaluated for the same conditions. For example if the effect of applied loads is to

produce compressive stress on a soil, it is obvious that this should be compared to the

bearing resistance of the soil, and not some other quantity. In other words, the

evaluation of the inequality must be done for a specific loading condition that links

together resistance and the effect of loads. Evaluating both sides at the same Limit

State provides this common link. When a particular loading condition reaches its

limit, failure is the assumed result, that is, the loading condition becomes a failure

mode. Such a condition is referred to as a limit state that can be defined as:


14/33



A limit state (in case of bridges) is a condition beyond which a bridge system or

bridge component ceases to fulfill the function for which it is designed.

Example of limit states for girder type bridges include:

Deflection, Cracking, Fatigue, Flexure, Shear, Torsion, Buckling, Settlement, Bearing, Corrosion, Sliding etc.Well defined limit states are established so that a designer knows what is considered

to be unacceptable.

An important goal of design is to prevent a limit state from being reached. However,

it is not the only goal. Other goals that must be considered and balanced in the overall

design are function, appearance, and economy.

It is not economical to design a bridge so that none of its components could ever fail.

Therefore, it becomes necessary to determine what is an acceptable level of safety or

probability of failure. The determination of an acceptable margin of safety (how

much greater the resistance should be compared to the effect of loads) is not based on

the opinion of one individual but based on the collective experience and judgment ofa qualified group of engineers and officials. In the highway bridge design community,

AASHTO (American Association of State Highway and Transportation Officials) is

such a group.


15/33



7. Design procedures:Over the years, design procedures have been developed by engineers to provide

satisfactory margin of safety. These procedures were based on the engineers

confidence in the analysis of the load effects and the strength of the materials being

provided. As analysis techniques improved and quality control on materials became

better, the design procedures changed. Two important design techniques/

philosophies are:

a. Allowable stress Design (ASD) design philosophy:The earliest design procedures were developed with the primary focus on metallic

structures kept in mind. Structural steel was observed to behave linearly up to a

relatively well defined yield point that was safely below the ultimate strength of

the material. Safety in the design was obtained by specifying that the effect of the

loads should produce stresses that were a fraction of the yield stress fy; say one

half. This value would be equivalent to providing as safety factor of 2, that is,

F = resistance (R)/ effect of loads (Q) = fy / (0.5fy) = 2

Because the specification set limits on the stresses, this became known as

allowable stress design (ASD).

Shortcomings of the ASD:

In the ASD method it is assumed that stress in the member is zero before anyloads are applied, that is, no residual stresses exist. The assumption is seldom

completely accurate.

ASD methods were developed for the design of statically determinate metallicstructures. They do not necessarily apply in a straightforward logical way to

other materials and other levels of redundancy.

The safety factor chosen is based on experience and judgment; quantitativemeasures of risk cannot be determined for ASD. Only the trend is known: if

the safety factor is higher, the number of failures is lower. However, if the

safety factor is increased by a certain amount, it is not known by how much

this increases the probability of survival. Also it is more meaningful to

decision makers to say. This bridge has a probability of 1 in 10,000 of failing

in 75 years of service, than to say, This Bridge has a safety factor of 2.3.


16/33



Allowable stress design does not recognize that different loads have differentlevels of uncertainty. Dead, live and wind loads are all treated equally in ASD.

The safety factor is applied to the resistance side of the design inequality, and

the load side is not factored.

b. LRFD Load Resistance Factor Design:In this method the resistance side of the basic equation is multiplied by a

statistically based resistance factor, whose value is usually less than 1, and the

load side is multiplied by a statistically based load factor, whose value is larger

than 1. Because the load effect at a particular limit state involves a combination of

different load types (Qi) that have different degrees of predictability, the load

effect side is represented by a summation ofiQi values. If the nominal resistance

is given by Rn, the safety criterion is:

Rn effect ofiQi

Because this equation involves both load factors and resistance factors, the design

method is called Load Resistance Factor Design (LRFD). The resistance factor

for a particular limit state must account for the uncertainties in

1. Material properties.2. Equations that predict strength,3. Workmanship,4. Quality control,5. Consequences of failure.The load factor chosen for a particular load type must consider the uncertainties

in:

1. Magnitudes of loads,2. Arrangement (positions of loads),3. Possible combination of loads.In selecting resistance factors and load factors for bridges, probability theory has

been applied to data on strength of materials, and statistics on weights of materials

and vehicular loads.


17/33



i. Advantages of LRFD: Accounts for variability of loads, Achieves fairly uniform levels of safety for different limit states bridge

types,

Provides a rational and consistent method of design.ii. Disadvantage of LRFD:

Requires a change in design philosophy, Requires an understanding of basic concepts of probability and statistics, Require availability of sufficient statistical data and probabilistic design

algorithms to make adjustments in resistance factors to meet individual

situations.

8. Important concepts in Bridge Engineering:Bridge: A structure having an opening not less than 6000 mm that forms part of a

highway or over, or under which the highway passes.

Collapse: A major change in geometry of the bridge rendering it unfit for use.

Design: Proportioning and detailing the components and connections of a bridge.

Design life: Period of time up on which the statistical derivation of a transient load is

based: 75 years for AASHTO specifications.

Service life: The period of time that the bridge is expected to be in operation.

Force effect: A deformation stress or stress resultant i.e. axial force, shear force,

torsional or flexure moment, caused by applied loads, imposed deformations or

volumetric changes.

Load factors: A factor accounting for variability of loads, the lack of accuracy in

analysis, and the probability of simultaneous occurrence of different loads.

Load modifier: A factor accounting for ductility, redundancy and the operational

importance of the bridge.

Resistance factor: A factor accounting for the variability of material properties,

structural dimensions, and the workmanship, and the uncertainty in the prediction of

resistance.


18/33



y

u

uP

Py

The resistance of components and connections is determined, in many cases, on the

basis of inelastic behavior, although the force effects are determined by using elastic

analysis in LRFD design specifications.

Limit state: A condition beyond which the bridge or component of the bridge ceases

to satisfy the provisions for which it was designed.

Strength limit state shall be taken to ensure that strength and stability, both local and

global, are provided to resist the specified statistically significant load combination

that a bridge is expected to experience in its design life.

Service limit state: The service limit state shall be taken as restriction on stress,

deformation and crack width under regular service conditions.

Fatigue limit state shall be taken as a set of restrictions on stress range due to a single

design truck occurring at the number of expected stress range cycles.

Fracture limit state shall be taken as a set material toughness requirements of

AASHTO material specifications.

Extreme event limit state shall be taken to ensure the structural survival of a bridge

during a major earthquake or flood, or when collided by a vehicle, vehicle or ice flow

under scored conditions.

Ductile behavior is characterized by the significant inelastic deformations before any

loss of load carrying capacity occurs.

The owner (of bridge) may specify a minimum ductility factor an assurance that

ductile failure modes will be obtained.

Ductility factor = u/ y

u = deformation at ultimate.

y = deformation at the elastic limit.


19/33



Traditional minimum depth (span to depth ratio) for constant depth super structure is

given as follows:

i. R.C.C Slabs:Simple span = 1.2(S + 3000)/30

= 1.2(S + 10)/30 (in fps system)

Continuous spans = (S + 3000)/30

ii. R.C.C T-Beams:Simple span = 0.070L

Continuous = 0.065L

iii. Prestressed I Beams:Simple span = 0.045L

Continuous spans = 0.040L

iv. Steel I Beams:Simple span (over all depth) = 0.040L

Continuous = 0.032L

v. Trusses = 0.100LMajor reason of Bridge failure: A majority of bridges that have failed in the United

States and else where have failed due to scour.

Permit vehicle: Any vehicle whose right to travel is administratively restricted in

anyway due to its weight or size.

Super structure: structural parts of the bridge which provides the horizontal span.

Sub structure: Structural parts of the bridge which supports the horizontal span.

Maximum ADT: Research has shown that average daily traffic ADT, including all

vehicles, i.e, cars and trucks, is physically limited to about 20,000 vehicles per lane

per day under normal conditions.

ADTT: Average daily truck traffic.

Compatibility: the geometrical equality of movement at the interface of joined

components.

Deformation: A change in structural geometry due to force effects, including axial

displacements, shears displacements and rotations.

Skin friction: acts upward on the side of piles or piers and thus supports the

foundation.


20/33



c/c distance between piles: It should be 750 mm (30) or 2.5 times pile dia.

Distance between centre of pile to edge of pile cap: should be 225 mm (9 inches)

Piers: The part of the bridge structure between the super structure and the connection

with the foundation.

Abutments: A structure that supports the end of a bridge span, and provides lateral

support for fill material on which the road way rests immediately adjacent to the

bridge.

Counterfort: A counterfort wall consists of a thin concrete face slab, usually vertically

supported at intervals on inner side by vertical slabs or counterforts that meet the face

slab at right angles.

Pile: A relatively slender deep foundation unit, wholly or partly embedded in the

ground, installed by driving, drilling, jetting or otherwise, and which derives its

capacity from surrounding soil and/or from the soil or rock strata below its tip.

Use of piles: piling should be considered when footings cannot be founded on rock,

stiff cohesive or granular foundation material at reasonable cost. Pile may be used as

a protection against scour.

Minimum design penetration (Embedment length in the soil):

3000 mm for hard cohesive or dense granular.

6000 mm for soft cohesive or loose granular.

Resistance of piles: shall be determined through subsurface investigations, laboratory

and/or in-situ tests, analytical methods, pile load test, and by referring to the history

of past performance.

Down drag: Down drag results from settlement of the ground adjacent to the pile or

shaft. It acts downward and loads the foundation.

9.

Important points for bridge design:

Road way widths: When the traffic is crossing the bridge, there should not be a sense

of restriction. To avoid a sense of restriction requires that the roadway width on the

bridge be the same as that of the approaching highway.

Loads: to be considered in bridge design can be divided into two broad categories:

Permanent loads, and, Transient loads.


21/33



Permanent loads: Self weight of girders and deck, wearing surface, curbs and parapets

and railings, utilities and luminaries and pressures from earth retainments.

Two important dead loads are:

DC: Dead load of structural components and non structural attachments.

DW: Dead load of wearing surface.

bitumen = 2250 kg/m3

= 22.1 kN/m3

concrete = 2400 kg/m3

= 23.6 kN/m3

The maximum load factor for DC = 1.25

The maximum load factor for DW = 1.5

Transient loads: Gravity loads due to vehicular, railway and pedestrial traffic. Lateral

loads due to water and wind i.e., floes (sheet of floating ice), ship collisions and

earthquake, temperature fluctuations, creep and shrinkage etc.

Some loads such as ship collision etc are important loads for substructure design.

The effects of these loads will be different for super structure and sub structure.

The automobile is one of the most common vehicular live load on most bridges; it is

the truck that causes the critical load effects.

AASHTO design loads attempt to model the truck traffic that is highly variable,

dynamic and may occur independent of, or in unison with other truck loads.

The principal load effect is the gravity load of the truck but other effects are

significant and must be considered. Such effect includes impact (dynamic effects),

braking forces, centrifugal forces (if present) and the effects of other trucks

simultaneously present.

Different design limit states may require slightly different truck models.

Design Lanes: The number of lanes a bridge may accommodate must be established

and is important design criterion. Two such terms are used in the lane design of the

bridge:

Traffic lane, Design lane.

Traffic lane: is the number of lanes of traffic that the traffic engineer plans to route

across the bridge. Lane width is associated with a traffic lane and is typically 3600

mm = 3.6 m = 12 ft.


22/33



Design lane: is the lane designation used by the bridge engineer for live load

placement. The design lane width and location may or may not be the same as that of

the traffic lane.

AASHTO uses a 3000 mm = 3.0 m = 10.0 ft design lane and Vehicles is to be

positioned within the lane for extreme effects.

No of Design lanes [A361.1.1] = Clear roadway width (mm) / 3600 mm = rounded to

larger integer.

Clear roadway width is the distance between the curbs or barriers.

When traffic lane width < 3600 mm

No. of design lanes = No. of traffic lanes, and

Width of design lane = Width of traffic lane

For roadway width from 6000 to 7200 mm (20 ft to 24 ft), two design lanes should be

used. And,

Design lane width = Roadway width

The direction of traffic in the present and future scenarios should be considered and

the most critical cases should be used for design. Additionally, there may be

construction and/or detour plans that cause traffic patterns to be significantly

restricted or altered.

Vehicular design loads: A study by the Transportation Research Board (TRB) was

used as a basis for AASHTO loads (TRB, 1990).

It was felt by the engineers developing the load model that the exclusion truck (over

loaded or more than allowed legally) best represented the extremes involved in the

present truck traffic (Kulicki 1992).

The AASHTO design loads model consists of three distinctly different loads:

Design truck,

Design Tandem, Design lane.

Design truck: The configuration of design truck as given in figure 14 is the same that

has been presented by AASHTO (1996) standard specifications since 1944 and


23/33



145 kN 145 kN 35 kN

4.3 to 9.0 m 4.3 m

32 k = 14.5 Tons

14' to 30' 14'

32 k = 14.5 Tons 8 k = 3.5 Tons

OR

1.2 m

110 kN 110 kN

4'

24 k = 11 Tons 24 k = 11 Tons

OR

commonly referred to as HS. The H denotes highway and S denotes Semi tractor and

20 is the weight of tractor in tons (USC units).

The new vehicle combination as described in AASHTO (1994) LRFD Bridge

specifications are designated as HL-93 for Highway Loading accepted in 1993.

Figure 14: Design truck.

The variable range, in figure 14 means that the spacing used should cause critical load

effect. The long spacing typically only controls where the front and rear positions of

the truck may be positioned in adjacent structurally continuous spans, such as

continuous short span bridges.

Design Tandem: The other configuration is the design tandem as shown in figure 15.

Figure 15: Design Tandem.


24/33



9.3 kN/m

0.64 k/ft

OR

Design lane load: 9.3 kN/m and is assumed to occupy a region of 3.0 m (10 ft). It is

applied as 3.1 kN/m2

or 0.064 k/ft2

(64 lb/ft2) of pressure to a width of 3.0 m or 10 ft

over the entire length of bridge for FEM.

Figure 16: Design lane load.

In summary three design loads should be considered: the design truck, design tandem,

and the design lane.

These loads are superimposed two ways to yield the live load effects, which are

combined with the other load effects (D loads) are:

Truck + lane, Tandem + lane,


25/33



S = 35 ft

Abutment 1 Abutment 2

2

1

H.W

(a) Elevation

Centreline of bridge

10' shoulder

12'

12'

10' shoulder

(b) Plan

15" W = 44' Roadway 15"

W = 46.5'

h (c) Section

1

3" F.W.S

Design Pb: Design the simply supported slab bridge of fig. 17, with a span length of 35 ft

centre to centre of bearings for a HL-93 live load. The roadway width is 44 ft curb to

curb. Allow for a future wearing surface of 3 inch thick bituminous overlay. Use fc =

4000 psi and fy = 60 ksi.

Figure 17: Solid Slab Bridge design example

Solution:

Step No 1: Sizes.

Span length of bridge (S) = 35 ft c/c

Clear roadway width (W) = 44 ft (curb to curb)

For a curb width of 15 inches, total width of the bridge (W1) = 44 + 2 15/12 = 46.5 ft

According to AASHTO (1994) LRFD Bridge specifications (table A.2.5.2.6.3-1),

minimum thickness of bridge slab is given by formula:


26/33



32 kip 32 kip 8 kip

S = 35'45.6 kip 26.4 kip

45.6 kip

13.6 kip

-18.4 kip

-26.4 kip

14' 14'3.5' 3.5'

158.1 ft-kip

350 ft-kip

90.56 ft-kip

hmin = 1.2(S + 10)/30

= 1.2 (35 + 10)/30 = 1.8 ft = 21.6 inches

Use h = 22 inches.

Step No 2: Loads.

Slab load (wDC) = (22/12) 0.15 = 0.275 ksf

Wearing surface load (wDW) = (3/12) 0.14 = 0.035 ksf

Step No 3: Analysis.

(1) Dead load moments:

Slab moments (MDC) = 0.275 (352)/8 = 42 ft-kip/ft

Wearing surface moment (MDW) = 0.035 352/8 = 5.3 ft-kip/ft

(2) Live load moments:

(a) Truck Load moments:

Figure 18: Shear force and bending moment diagrams for truck load.

Therefore, MTruck= 350 ft-kip


27/33



35'

640 lb/ft

4'

24 kip 24 kip

35'

(b) Lane moment:

Mlane = 640 352/8 = 98 ft-kip

Figure 19: Lane load.

(c) Tandem moment:

Mtandem = 372 ft-kip

Figure 20: Tandem load.

Mtandem > Mtruck

Therefore we will use Mtandem

MLL+IM (Including impact) = 1.33Mtandem + Mlane

[MLL+IM

= 1.33 372 + 98 = 593 ft-kip]

Now converting MLL+IM to moment/ft, Divide MLL+IM by E design lane width.

Note: While calculating truck/tandem (live load) moments, it has been assumed that axle

load is acting as a point load. However in reality the vehicle will occupy some definite

width, hence this live load moment must be divided by this width. AASHTO LRFD gives

following procedure for converting this moment to per foot width. Similarly AASHTO

LRFD also emphasizes that live load will produce different effects on interior and edge

strips of slabs as shown below.

Design Lane width E for interior strip:

(a)For single lane loaded:E = 10.0 + 5.0 (L1W1)

L1 = Modified span length = Minimum of (S = 35 ft) and 60 ft

L1 = 35 ft

W1 = Modified edge to edge width = Minimum of (W1 = 46.5 ft) or 30 ft


28/33



W1 = 30 ft

Therefore, E = 10.00 + 5.0 (35 30.00) = 172 in = 14.3 ft

(b)For multilane loaded:E = 84 + 5.0 (L1W1) W/NL

L1 = 35 ft

W1 = Minimum of (W1 = 46.5 ft) or 60 ft

W1 = 46.5 ft

NL = No. of design lanes.

NL = INT (W/12) =INT (44/12) = 3

Therefore, E = 84 + 1.44 (35 46.5) 46.5/3

= 142 inch or 11.84 ft 15.5

Therefore, E = 11.84 ft (Least of all)

Hence interior strip moment per foot width is equal to:

MLL +IM (Interior strip) = 593/11.84 = 50 ft-kip/ft

Now,

Mu = 1.05 (1.25MDC + 1.5MDW + 1.75MLL+IM)

Mu = 1.05 (1.25 42 + 1.5 5.33 + 1.75 50)

Mu(interior strip) = 155.3 ft-kip/ft = 1863.6 in-kip/ft

Design lane width for edge strip: According to AASHTO LRFD code A4.6.2.1.4,

E = Barrier width at base + 1 ft + (1/2) strip width Full strip width or 6 ft

(whichever is less)

Therefore E = 1.25 ft + 1 ft + (1/2) 11.84 11.84 ft or 6ft

E = 8.17 ft > 6 ft

Therefore E = 6 ft

Because the strip width is limited to 6, one-lane loaded (wheel line = lane load)

with a multiple presence factor, m (chapter 4, Barker and Puckett) of 1.2 will be

critical. Hence edge strip moment per foot width is equal to:

MLL+IM (Edge strip) = (593) 1.2/6 = 59.3 ft-kip/ft

Mu = 1.05 (1.25MDC + 1.5MDW + 1.75MLL+IM)

Mu = 1.05 (1.25 42 + 1.5 5.33 + 1.75 59.3)

Mu (edge strip) = 172.48 ft-kip/ft = 2069.79 in-kip/ft


29/33



15" 12'/2 = 6'

6' maximum

12"

Lane load

Wheel lines

Figure 21: Live load placement for edge strip.

Step No 4: Design.

(a) Design for Interior strip:

Interior strip moment (Mu) = 155.3 ft-kip/ft = 1863.6 in-kip/ft

Effective depth of bridge slab (d) = h cover Dia of bar used

Using #8 bar, effective depth is:

Bottom cover for slab is taken equal to 1 inch.

d = 22 1 1 = 20.5 inch

Asmin = 0.0018 12 22 = 0.47 in2

As

= Mu/{f

y(d a/2)}

Let a = 0.2d = 0.2 20.5 = 4.1 inches

Therefore,

As = 1863.6/{0.9 60 (20.5 4.1/2)} = 1.87 in2

> Asmin

Trial 1:

a = Asfy/(0.85fcb) = 1.87 60/ (0.85 4 12) = 2.75 inch

As = 1863.6/{0.9 60 (20.5 2.75/2)} = 1.804 in2

Trial 2:

a = 1.804 60/ (0.85 4 12) = 2.65 inch

As = 1863.6/{0.9 60 (20.5 2.65/2)} = 1.80 in2, O.K.

Use #8 bar with bar area = 0.79 in2

Spacing = (0.79/1.80) 12 = 5.33 inches 5 inches c/c

Use #8 @ 5 inches c/c.


30/33



(b) Distribution reinforcement for interior strip (bottom transverse reinforcement)

{A5.14.4.1}:

The amount of bottom transverse reinforcement may be taken as a percentage of

the main reinforcement required for positive moment as

100/L 50 %

100/L = 100/35 = 16.9 % < 50 %

Therefore, bottom transverse reinforcement = 0.169 1.80 = 0.304 in2

Using #5 bar, with bar area = 0.31 in2

Spacing = (0.31/0.304) 12 = 12 inches c/c

Maximum spacing for temperature steel reinforcement in one way slab according

to ACI 7.12.2.2 is minimum of:

(i) 3hf=3 22 = 66(ii)18

Finally use #5 @ 12 inches c/c.

(c) Design for Edge strip:

Edge strip moment (Mu) = 172.48 ft-kip/ft = 2069.79 in-kip/ft

Effective depth of bridge slab (d) = h cover Dia of bar used

Using #8 bar, effective depth is:

Bottom cover for slab is taken equal to 1 inch.

d = 22 1 1 = 20.5 inch

Asmin = 0.0018 12 22 = 0.47 in2

As = Mu/{fy (d a/2)}

Let a = 0.2d = 0.2 20.5 = 4.1 inches

Therefore,

As = 2069.79/{0.9 60 (20.5 4.1/2)} = 2.00 in2 > Asmin

Trial 1:

a = Asfy/(0.85fcb) = 2.00 60/ (0.85 4 12) = 2.94 inch

As = 2069.79/{0.9 60 (20.5 2.94/2)} = 2.014 in2

Trial 2:

a = 2.014 60/ (0.85 4 12) = 2.96 inch


31/33



As = 2069.79/{0.9 60 (20.5 2.96/2)} = 2.014 in2, O.K.

Use #8 bar, with bar area = 0.79 in2

Spacing = (0.79/2.014) 12 = 4.7 inches 4.5 inches c/c


(d) Distribution reinforcement for edge strip:

Bottom transverse reinforcement = 0.169 2.014 = 0.34 in2


Maximum spacing for temperature steel reinforcement in one way slab according

to ACI 7.12.2.2 is minimum of:

(i) 5hf= 3 22 = 66(ii)18Finally use #5 @ 8 inches c/c.

(e) Shrinkage and temperature reinforcement in top of slab (long and transverse both):

For grade 60 steel,

Ast = 0.0018Ag = 0.0018 12 22 = 0.47 in2

Use #5 bars, with bar area = 0.31 in2



Final Recommendation:

Main steel (bottom) = #8 @ 4 c/c for interior as well as exterior.

Transverse bottom reinforcement = #5 @ 8 c/c throughout.

Top steel (long and transverse) = #5 @ 8 c/c.


32/33



15" W = 44' roadway 15"

W = 46.5'22"

Transverse Section.

3" F.W.S34"

22"

#5 @ 8" c/c #5 @ 8" c/c

#8 @ 4" c/c3.5"

#5 @ 8" c/c

46.5'/2 = 23.35'

Step No 5: Drafting.

Figure 22: Reinforcement details in half transverse section.


33/33


References

Design of Concrete Structures by Nilson, Darwin and Dolan (13 th ed.),

Design of Highway Bridges by Richard M. Barker.

Documents

Inroduction to Bridge Engineering