strength assessing of bridges

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STRENGTH ASSESSMENT OF BRIDGE STRUCTURES


1.0 SUMMARY

Maintenance of bridge structures is an involved task of multiple disciplinary natures.

This includes inspection, assessment of strengths, repairs and maintenance, rehabilitation,

optimisation of resources, proper documentation and interaction with external bodies and

public.

A structure is called deficient when it has been restricted to reduced load level only,

closed, or required immediate rehabilitation to keep it open. The structure can be calledfunctionally obsolete when it no longer safely service the system of which it is an integral

part. For a bridge structure, the deficiency in any one or a combination of the following will

be responsible to be called as functionally obsolete : a) deck geometry, b) load carrying

capacity and c) approach roadway alignment. The obsolescence or the state of deficiency of

the structure should not be declared by an individual, rather a consensus of an expert

committee should be taken before taking any decision, because it varies significantly due to

the criteria and different analytical procedures used for estimation.

Assessment of existing bridges and strengthening for structural deficiency have

become major components of modern bridge engineering. But just as it is important not to

over-design new structures, responsible engineers should not apply excessively conservative

methods to assessment: in many cases a refined, more accurate method can show that the

existing structure has sufficient capacity, requiring no strengthening. This not only saves the

often considerable costs associated with strengthening or replacement, but also extends the

life of the existing structures, saving resources and promoting sustainability

To keep the bridge structure in safe and serviceable condition, the structural elements

have to be inspected periodically to study the behaviour, performance, safety and interaction

in the structural system. The strength assessment and rehabilitation should not be done only

based on the visual inspection of the structures.

Review of the serviceability condition of the modern bridges reveals that most

problems stem from the deterioration of materials. Structural analysis for determining the

strength of bridges plays an important role in the assessment and rehabilitation of bridges.

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2.0 INTRODUCTION

Bridges are vital elements for road and rail network for overall societal and national

development, and hence call for regular maintenance, strengthening and rehabilitation works.

Overseeing organisation are developing comprehensive programmes for bridge assessment

and strengthening.

Most bridge owning authorities are well progressed with their bridge assessment

programmes. However they are now facing up to the task of dealing with the backlog of

structures that have failed their original assessment. Many of these have been placed into the

basket for "future strengthening or replacement" or for "monitoring and re-assessment" based

on the "engineering judgement" of the bridge engineers who have had to prioritise their

scarce resources for strengthening and replacement works. However at some stage all of these

"failed" bridges must still be re-assessed and a decision taken on what action is required to

ensure their structural integrity and safety.

The causes of failure are varied and depend very much on the type of structure and

also, to an extent, on age and location. For example most of the motorway and trunk road

bridges were built post-1960 during the motorway expansion schemes. These bridges are

predominantly concrete and the Highways Agency is concerned with problems such as

deficiencies in shear, flexural capacity, inadequate anchorage details, pre-stress corrosion and

deterioration of joints, piers and cross-heads. Local authorities, on the other hand, have large

numbers of masonry arch bridges, which pose particular analysis problems, and also many

older concrete bridges which have often been subject to significant deterioration or were

designed with inadequate detailing, little or no top steel, and low percentages of transverse

steel.

The aim of these programmes is to bring the bridge stick up to the modern standards

to ensure it could safely carry the desired vehicles load.

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3.0 PRIMARY ISSUES TO BE CONSIDERED IN BRIDGE PERFORMANCE AND

RELEVANT FACTORS FOR THE STRENGTH ASSESSMENT

1. Structural Condition & Structural Integrity

Structure type

Structural materials & material specifications

Vertical clearances over & under

As-built material qualities & current conditions

As-built construction qualities & current conditions

Traffic loads trucks

Environment climate, air quality, marine atmosphere Snow & ice removal operations

Type, timing & effectiveness of preventive maintenance

Type, timing & effectiveness of restorative maintenance, minor & major

rehabilitation

Hydraulic design and scour mitigation measures

Soil characteristics settlement

2. Safety (of Users)

Structure geometry- clear deck width, skew, approach roadway alignment

Vertical clearances over & under

Traffic volumes and percentage of trucks

Posted speed

3. Costs

Initial construction costs

Maintenance, repair & rehabilitation costs

Traffic maintenance costs

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4.0 BRIDGE INSPECTION FLOWCHART

The purpose of strengthening and assessment is to ensure the following points.

1. Duty of care- To ensure that the part of the road supported by the bridges is safe for

those who are likely to use it.

2. For traffic- To ensure that operational capacity available reflects the needs of road

network users.

3. Financial- To ensure that the whole life of the bridge stock is either enhanced or

stabilised (not reduced), as a result of financial expenditure on maintenance.

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BRIDGES AND

PRINCIPAL

INSPECTIONROUTINE

INSPECTION

SPECIAL

INSPECTION

STRUCTURAL

DEFICIENCY

ASSESSMENT

/

EXECUTION

OF

ROUTINE

MAINTENANCE


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The concept of whole lifecycle cost relates to the design, construction and subsequent

maintenance of the bridges. The factors governing the strategies and the bridge management

philosophies of the overseeing organisation are the discount rate and road user delay costs.

The introductions of design and build projects, and the different permutation of finance,

operate and transfer presents an opportunity to take the maintenance aspect of the bridge

structures.

Rehabilitation and strengthening of the bridge structures is generally an approach based

on policy factors. It aims to funnel resources projects of recognised importance at the

expense, but not the abandonment, of project of lesser importance.

5.0 BRIDGE MANAGEMENT

Strength assessments are completed on existing bridge structures to determine the

optimum long-term solution for maintenance, rehabilitation or replacement to maximize the

service life of the structure at a minimum life cycle cost. The assessment is intended to

develop a strategy that answers what, when and how much.

The Department identifies bridge structures that may require maintenance,

rehabilitation or replacement in a short-term programming period. Structures may beidentified for an assessment based on condition deficiencies, functional deficiencies or

proposed highway improvements. There are three types of assessments, Bridge Assessments,

Rehabilitation Assessments and Complex Assessments, which are defined in more detail

below.

To determine the need for an assessment, an internal review applying appropriate

screening criteria should be completed. If the appropriate course of action is readily identified

at the screening phase, an assessment will not be required. This best practice guideline has

been adopted to provide guidance on when a particular type of assessment should be

completed and to define what each type involves.

A Bridge Assessment may be initiated due to the existing condition of the structure or

proposed highway improvements. For the Bridge Assessment, the Departments internal

review of the existing structure will indicate that replacement may be economically feasible

or that functional improvements should be considered.

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The assessment should include the following areas:

summary of bridge condition

proposed highway improvements (if applicable)

functional deficiencies (width, strength, vertical clearance)

environmental (identification of issues and likely impacts)

1 navigability

2 fisheries

hydro technical

3 adequacy of existing structure (risk of flooding or failure)

4 replacement structure sizing

alternatives

5 actions, timing and cost estimates

6 life cycle cost analysis

recommendation

6.0 BRIDGE MANAGEMENT FLOW.

1. TOP DOWN APPROACH:

Budgets and standards are used to develop optimal policies which are then used to

plan projects. Feedback is provided to refine the models. Budgets and standards may be

modified to perform what if analysis.

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POLICIES

BUDGE STANDAR


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2 BOTTOM UP APPROACH:

Standards assist in planning projects. Planned projects are totalled to generate costs

which are then compared to budgets. This is used to adjust the standards and modify the

plans.

7.0 REQUIREMENT FOR STRENGH ASSESMENT

Strength assessment of whole structures or of critical elements is carried out in

accordance with the technical requirement specified by overseeing organisation.

An assessment constitutes a present state evaluation of all parts of a structure that

act monolithically and carry primary live load. For a bridge, this includes superstructure and

elements of the substructures. Precise details assessment are agreed for a particular structures

through the Approval in Principal or the assessment basis note.

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PROJECTS

BUDGE

COSTS

PROJECTSTANDARD


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The process of strength assessment is a complete evaluation of the safe load carrying

capacity of the structures. The assessment reports on the adequacy of different parts of the

structures and identifies critical elements of the structure for subsequent inspection,

assessment and rehabilitation works. Other safety considerations, such as weak parapets may

also be considered during strength assessment.

A particular assessment may be required to assess the critical section or the elements

of the structure identified from the periodic process of assessment process. It is generally

carried out following special inspection and takes into account any deterioration identified in

the special inspection. The particular assessment utilizes available data and information from

the periodic assessment report. The intention is to reduce the amount of calculation necessary

and ensure that assessment calculations are acceptable and available to all. Furthermore,

careful consideration is given to validity of the approach for a particular structure, as it is

dependent on the structural modelling techniques and the nature and extent of component

deterioration.

PROCESS FLOW FOR ASSESSMENT OF BRIDGES

8.0 UNCERTAINITIES IN STRENGTH ASSESSMENT

It is ironic, however, that the general view held by many engineers is that strength

assessment is more difficult task than initial design. Yet in the former case, the structure

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NEED FOR

BRIDGEASSESSMENT

PREPERATION

OFASSESSMENT

ANALYSIS FOR

DETERMNITIONOF LOAD

RECOMMENDATIO

N FOR

STRENGTHENING

DETERMINATIO

N OF

UTILISATION

AND RESERVE

COMPUTATION

OF SECTION

CAPACITIES


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physically exists and is available for the study, testing and measurement, whereas in case of

new design the structure exists only in the form of drawings,calulation and specifications.

Most of the uncertainities are time dependent. Such as decrease in strength of construction

materials like concrte, steel etc. Uncertainity may be variation of present traffic loading and

assessing of future intensity of traffic for the design period of bridge structure. Using these

inadequate strength of materials and varying traffic loading data the determination of reserve

strength or the strength of assessment of bridge structures become difficult.

9.0 STRENGTH ASSESSMENT OF CONSTRUCTION MATERIALS OF BRIDGE

STRUCTURES

Strength of construction materials of bridge structures are mainly assessed by the non

destructive test methods. Non-destructive test methods for concrete may be classified in two

categories. The estimation of strength of concrete is the major objective of non-destructive

tests. The characteristic strength of the concrete is estimated based on the calibrated 28 days

characteristic strength with appropriate reading of that method. In every method, a calibration

of the instrument has to be established before performing the test. The surface hardness,

penetration resistance, pullout, break-off, pull-off and maturity techniques belong to this

category. The other category includes different methods such as stress wave propagation,

ground probing radar and infrared thermograph techniques, which are used to locate

delaminations, voids, and cracks in concrete. Another important for strength assessment

would be details of steel reinforcement such as bar location, bar size and corrosion in steel.

There are different instruments available in the market to determine the above details.

9.1 SURFACE HARDNESS METHOD

The Schmidt rebound hammer is mainly a surface hardness tester. An empirical

correlations have been established between strength property and rebound hammer. The

rebound number is measured on an arbitrary scale marked from 10 to 100. The plunger is

released from its locked position by pushing the plunger against the concrete and slowly

moving the body away from the concrete. The test can be conducted horizontally, vertically

upward or downward or at any intermediate angle. However, in each case a separate

calibration has to be made because the rebound number will be different in the same concrete

due to different effects of gravity. . However, it has some limitations. The results of the

Schmidt rebound hammer are affected by: a) smoothness of test surface, b) size, shape and

rigidity of specimens, c) age of test specimens, d) surface and internal moisture conditions of

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the concrete, e) type of coarse aggregate, f) carbonation of concrete surface. It may be noted

that this test method is not intended as the basis for acceptance or rejection of concrete

because of the inherent uncertainty in the estimated strength. It is possible to estimate of the

strength of concrete within 15 to 20% by the rebound hammer provided the specimens are

cast, cured and tested under conditions similar to those from which the correlation curves are

established.

9.2 THE ULTRASONIC PULSE VELOCITY METHOD

. In the ultrasonic pulse velocity test method, an ultrasonic wave pulse through

concrete is generated at a point on the surface of the test object and the time of travel between

the transmitting point and receiving point is measured. It is relatively easy to conduct a pulse

velocity test. However, it should be noted, that pulse velocity is affected with the concrete

properties, such as, aggregate size, grading, cement type, water-cement ratio, admixtures or

age of concrete, The pulse velocity also changes with the transducer contact, temperature of

concrete, moisture and curing condition of concrete, size and shape of specimen and the level

of stress. The estimation of compressive strength of concrete from pulse velocity is only

possible when a similar correlation has been previously established. In general, it is more

qualitative.

9.3 MAGNETIC METHOD

Magnetic non-destructive testing techniques used in conjunction with concrete

involve the magnetic properties of the reinforcement and the response of the hydrogen nuclei

to such field. The location, sizes, and depth of reinforcement are determined on the basis of

magnetic induction principle. Commercial reinforcement bar locators are portable,

inexpensive instruments and the accuracy of 2% or 2.5 mm up to depths of 150 mm has

been claimed.

9.4 ELECTRICAL METHOD

The durability of concrete can be estimated by measuring the changes in electrical

properties of concrete. Moist concrete behaves essentially as an electrolyte with a resistivity

in the order of 104 ohm-cm. Oven-dried concrete has a resistivity in the order of 1011 ohm-cm.

The resistance probe method involves measuring the electrical resistance of a material, which

decreases as the moisture content increases. Most instruments consist of two closely spaced

probes and a meter battery assembly enclosed in a housing. The moisture content at various

depths can be measured by penetrating the probe.

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9.5 RADIOACTIVE METHOD

Gamma radiometry is widely used in highway construction for density determinations on

soil, soil aggregates and asphalt concrete. It is just beginning to gain acceptance for testing

concrete. All gamma radiometry systems are composed of (a) a radioisotope source of

gamma rays, (b) the concrete being examined, (c) a radiation detector and counter.

The principal applications of radiography to concrete to date are primarily in two categories :

(a) X-, gamma and neutron radiography in laboratory studies of internal microstructure,

particularly micro cracking. and (b) X- and gamma radiography in field studies of

microstructure, e.g., the location of reinforcing steel and voids or areas of inadequate

consolidation

10.0 NOTES ON UTILISTION, RESERVE FACTOR AND LIVE LOAD FACTOR

Utilisation factor (UF) is defined as the ratio of the load effects (due to permanent and

live loads) and section capacity (i.e. the strength).

UF= (permanent load effects+ live load capacity) / (assessed section capacity).

Reserve factor (RF) is defined as the factor of assessment live load required to reach

the first failure. It is the ratio of section capacity less the permanent load effects and the live

load effect.

RF= (Assessed section capacity-permanent load effects) / (assessed live load effects).

Live load factor is defined as the ration of live load to dead load. Clearly the higher

the live load factor would mean that the bridge is less sensitive to increased loads.

LLF= (Live load / Dead load).

11.0 ANALYSIS FOR STRENGTH ASSESSMENT

Structural analysis for assessment and strengthening of the bridges aims to determine

the reserve strength of the structures by optimising the use of available analytical methods

and analysis tools. It has been observed that if the assessment is excessively conservative

then an adequate structure may be condemned as Safe.

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The method of analysis should be appropriate for the bridge under the consideration

for assessment. It is recommended to comment an assessment with a simple method of

analysis and then to extend the analysis if there short fall in the capacity.

It is generally observed that the concrete bridges carry loads much greater than the

design loads due to their capacity to redistribute the load effects. This reserve strength of

concrete bridge is largely due to redistributions of the load effect, resulting from the available

ductility and redundancy, which results in a sizeable difference between the first yield load

and ultimate collapse load. In order to utilise this reserve strength of the concrete bridges, the

analysis of the structure and the computation of cross section capacities should adopt non-

linear or plastic method of analysis. However the use of non-linear or the plastic method of

analysis should ensure the availability of the adequate ductility of the concrete structures. In

some cases it is observed that the structure may have adequate strength at the ultimate limit

state but may show distress at serviceability limit state and the structure may deemed unsafe

or its usage may be restricted.

11.1 SELECTION OF METHODS FOR ANALYSIS OF STRENGTH ASSESSMENT

There is an underlying realisation that the analytical techniques developed for design

are in many cases unable to accurately model the structural behaviour of existing bridges. Asa result assessments often significantly underestimate the actual load capacity of bridges.

This discrepancy between theoretical predictions and reality has been highlighted by the

number of bridges which have failed their assessment even though the assessing engineers'

experience and intuitive feelings tell them that the bridges are capable of safely carrying

significantly higher loads. There are examples cited of bridges which have regularly carried

abnormal vehicles weighing 180 tonnes without distress being assessed to have an ultimate

load capacity of 7.5 tonnes. Equally most bridge engineers will know of examples of

assessment reports in which concrete slab bridges have been rated at zero live load capacity.

In many cases, the bridges exhibit no outward signs of distress. Although this does

not, in itself, imply that failure may not be imminent, it is likely that some evidence of

damage or significant deformation will precede collapse in cases of ductile flexural failure of

concrete slabs.

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3. Plastic methods: In this method of analysis, a part of or all of a material in the

section or sections of a structural member is assumed to have reached its yield

point under the applied loading. This results in possibility of plastic hinge or yield

lines being formed in the structures where yielding has taken place.

Analysis of the structure at ultimate limit state, determines the load effects under the

most adverse of the prescribed design loading conditions by a method satisfying the

equilibrium requirements. Usually the underlying theory for such analysis is plastic theory.

However elastic analysis methods are also applicable as lower bound solution for the

assessment of the strength of the structure.

Analysis of the structure at serviceability limit state, determines the load effects under

the prescribed design loading conditions by elastic method. However, non-linear methods

may be adopted with appropriate allowance for loss in stiffness due to cracking, creep, or

other predictable deformations of the structure and should be used where geometric changes

significantly modify the load effects.

Plastic method of analysis implicitly assumes that the structure is ductile. Concrete

structures are generally sufficiently ductile for this assumption to be valid. However,

establishing precise bounds on the ductility requirements for plastic analysis to be valid isquite complex. Non-linear numerical methods such as non-linear finite element analysis, can

be used to account for the effects of limited ductility. However, such methods can be highly

complex and, therefore, costly to apply, and particular care and expertise is require to ensure

that the results are reliable.

One of the major differences between the design and assessment lies in the fact that

assessment are undertaken on the actual structures that have typically been in service for

some years. As a result of their condition may not be as it was intended when designed either

as a result of construction error or subsequent deterioration. Assessment should be

undertaken on basis of the actual properties of the structures, as built and matured.

11.2.1 ELASTIC METHOD OF ANALYSIS- A CONVENTIONAL APPROACH OF

ASSESSING LOAD CAPACITY.

Current codes of practice are written with the implicit assumption that the design and

assessment of bridges will usually be undertaken using linear elastic analysis techniques.Elastic theory is well established and understood, is supported by many computer software

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packages, and has been found most satisfactory for the design of bridges. As a lower-bound

method the engineer can be confident that the analysis method should be conservative and

hence safe.

This approach is quite understandable for design where a certain degree of

conservativeness costs relatively little. Typically, the engineer might initially perform a

simple elastic beam analysis using a representative strip of the bridge deck. If this quick

check shows the structure to be inadequate, a more detailed linear elastic analysis allowing

for transverse distribution of load would probably be performed using either a grillage or

finite-element analysis. These results are then examined to identify individual locations at

which the maximum calculated moments or shears exceed the estimated ultimate capacity of

the section.

The decision to strengthen or replace a structure is commonly made on the basis of

these results. However, many older reinforced concrete bridges in the U.K. were built with

little or no top steel and very little transverse steel. Such structures almost inevitably are rated

at very low flexural capacities using such an elastic failure criterion when, for example, the

live load is positioned to one side of the deck resulting in some hogging or transverse sagging

moments.

In reality, concrete structures will crack under heavy loads resulting in a change in the

stiffness of the slab. Even when the ultimate moment capacity of a section of the deck is

exceeded loads will be redistributed elsewhere in the slab provided sufficient ductility is

available and it does not fail prematurely in shear. As a result, a linear elastic analysis will

not accurately model the distribution of stresses or the actual behaviour in the post-elastic

range where non-linear effects dominate. Elastic methods can be very conservative since

failure of one element in the structure is typically used to define failure of the structure as a

whole. In the cases of flexural failure, the consequences are likely to be small and may only

affect the serviceability of the structure. If one accepts that serviceability criteria do not

govern and collapse is the criterion on which to base the assessment, such conservativeness is

not warranted for concrete slab bridges for which ductile flexural failure is the critical

mechanism of failure. Once an individual section has reached ultimate or yielded, the failure

must develop into a full collapse mechanism before the structure will actually fall down.

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Despite the enormous cost implications of adopting such an approach, elastic methods

are still relied upon as the primary analysis tool for assessing concrete deck slabs. This is

despite the fact that there is a wealth of evidence from model experiments and full-scale load

tests to show that concrete bridges are often able to carry loads well in excess of the

theoretical capacity calculated using elastic techniques.

It is thus important to investigate the options available to an engineer if, after

performing an elastic analysis, the structure still fails to comply with the required standards.

The only practical alternatives to elastic analysis would involve undertaking a more

sophisticated analysis of the ultimate strength of the bridge or else carrying out load tests on

the bridge itself as a means of verifying the load capacity. In the research environment, wherethe best possible predictive methods are sought to model the actual behaviour of bridges,

researchers have, almost without exception, used yield-line theory, and in more recent years

non-linear finite element methods, to predict the flexural collapse behaviour of concrete slabs

and concrete bridge decks.

11.2.1.1 LINE BEAM ANALYSIS OR STRIP ANALYSIS METHOD

The line beam analysis for slab and beam structures determines the load effects in the

beam using the static load distribution, ignoring the capacity of the deck to distribute the

load. This is lower bound method of analysis. If a structure deemed safe according to this

method of analysis, we should avoid more sophisticated analysis. The disadvantage of this

method of analysis is that the analysis does not give load effects in transverse direction.

This method is very useful as an independent check when more sophisticated methods

are used.

11.2.1.2 ELLASTIC GRILLAGE

Elastic grillage is one of the most commonly used method for analysis of bridge

structures. The advantage of grillage over line beam method lies in its ability to cater for the

distributions of the loads between the beams through the transverse members. Hence the

grillage method is superior method of analysis only when the structure has adequatetransverse rigidity to allow redistribution of loads.

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The section properties of grillage elements influence the outcome of analysis to a

large extent. In elastic method of analysis one had the liberty to choose the type of section

properties i.e. cracked or un-cracked section properties. However it is to be noted that in

design, one is restrict to the use of un-cracked section properties as the same can only be

computed after the amount of reinforcement required has been determined.

In isotropic structures, the use of cracked or un-cracked section properties makes no

difference as the stiffness in either direction is equally affected. However, in practise most

bridge structures are non-isotropic and, hence, the choice of type of stiffness has considerable

effect.

The grillage analysis results are also sensitive to the torsion characteristics used in

sectional properties. The assignment of torsional sectional properties should aim to optimise

the use of torsional and bending capacity of the section.

Grillage analysis is essentially a computer-aided method for analysis of bridge decks.

The deck is idealized as a series of beam elements (or grillages), connected and restrained at

their joints. Each element is given an equivalent bending and torsional inertia to represent the

portion of the deck which it replaces. Bending and torsional stiffness in every region of slab

are assumed to be concentrated in nearest equivalent grillage beam. Restraints, load andsupports may be applied at the joints between the members, and members framing into a joint

may be at any angle.

BASIC THEORY OF GRILLAGE ANALYSIS

Basic theory includes the displacement of Stiffness Method. Essentially a matrix

method in which the unknowns are expressed in terms of displacements of the joints. The

solution of the problem consists of finding the values of the displacements which must be

applied to all joints and supports to restore equilibrium.

SLAB IDEALIZATION- SPACING AND LOCATION OF GRILLAGE

MEMBERS

The logical choice of longitudinal grid lines for T-beam or I-beams decks is to make

them coincident with the centre lines of physical girders and these longitudinal members are

given the properties of the girders plus associated portions of the slab, which they represent.

Additional grid lines between physical girders may also be set in order to improve the

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accuracy of the result. Edge grid lines may be provided at the edges of the deck or at suitable

distance from the edge. For bridge with footpaths, one extra longitudinal grid line along the

centre line of each footpath slab is also provided. The above procedure for choosing

longitudinal grid lines is applicable to both right and skew decks.

When intermediate cross girders exist in the actual deck, the transverse grid lines

represent the properties of cross girders and associated deck slabs. The grid lines are set in

along the centre lines of cross girders. Grid lines are also placed in between these transverse

physical cross girders, if after considering the effective flange width of these girders portions

of the slab are left out. If after inserting grid lines due to these left over slabs, the spacing of

transverse grid lines is still greater than two times the spacing of longitudinal grid lines, the

left over slabs are to be replaced by not one but two or more grid lines so that the above

recommendation for spacing is satisfied

When there is a diaphragm over the support in the actual deck, the grid lines

coinciding with these diaphragms should also be placed. When no intermediate diaphragms

are provided, the transverse medium i.e. deck slab is conceptually broken into a number of

transverse strips and each strip is replaced by a grid line. The spacing of transverse grid line

is somewhat arbitrary but about 1/9 of effective span is generally convenient. As a guideline,

it is recommended that the ratio of spacing of transverse and longitudinal grid lines be kept

between 1 and 2 and the total number of lines be odd. This spacing ratio may also reflect the

span width ratio of the deck. Therefore, for square and wider decks, the ratio can be kept as 1

and for long and narrow decks, it can approach to 2.

The transverse grid lines are also placed at abutments joining the centre of bearings.

A minimum of seven transverse grid lines are recommended, including end grid lines. It is

advisable to align the transverse grid lines normal to the longitudinal lines wherever cross

girders do not exist. It should also be noted that the transverse grid lines are extended up to

the extreme longitudinal grid lines.

GRILLAGE MESH (SIMPLE)

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BRIDGE DECK IDEALIZED MODEL (DEFLECTED)

11.2.1.3 INFLUENCE SURFACE CHARTS

The elastic analysis of slab may also be done by using standard influence surface

charts. These are two dimensional equivalent of influence lines. They plot the bending

moment intensity, for example, at a particular point in a slab due to point loads applied at all

positions in the slab. The most commonly used surface charts are that by Pucher.

11.2.2 PLASTIC EQUILLIBRIUM METHOD OF ANALYSIS

The upper bound theorem of plastic limit analysis underpins many of the approaches

used in the design of structures, particularly elastic methods. It is important to recognise that

this is strictly applicable to ductile structures and for cases where displacements are small.

Furthermore, it is essential that the equilibrium is satisfied everywhere throughout the

structure.

The ductility of reinforced concrete sections in flexure can be assessed from their

rotation capacity. The rotation capacity of the concrete section is governed either by concrete

crushing or reinforcement fracture. Particular care should be taken when considering the

structures which are either heavily reinforced or which are lightly reinforced with

reinforcement that itself has limited ductility. Structures that are moderately reinforced

typically have high degree of ductility, making them suitable for plastic analysis.

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11.2.2.1 YIELD LINE ANALYSIS

Yield-line method is a long established method of using the plasticity of reinforced

concrete slabs in order to obtain greater capacity than that obtained by elastic analysis.

Geometrically compatible plates of bridge deck are deflected under load to simulate a

failure mechanism. Each plate is bounded by straight lines and the boundaries form the

plastic hinges with the reinforcement yielding such that the mechanism is formed. The work

done in deflecting the load is deflected to the work done in yielding the reinforcement along

the plate boundaries.

This method provides an upper bound solution so it is necessary to examine all

conceivable combination and permutation of plate configurations to determine the failure

mode which gives the lowest ratio of applied work to internal work. Higher partial safety

factors are usually used for yield-line analysis in order to allow for this uncertainty. In

practise yield line analysis is generally used when elastic analysis has failed to show adequate

strength.

Yield line analysis is a familiar technique for determining the bending strength of

concrete bridge slabs (Johansen 1962; Clark 1983) but is generally not used in practise.

Probably because it is an upper bound method and also because many possible mechanism

have to be investigated in order to find the critical one. Many engineers find it tedious and

complex. However, providing that the slab is of simple geometry and possess sufficient

ductility for a mechanism to form, it could be used when conventional elastic techniques

indicate inadequate bending strength. A separate check is required for shear using

conventional elastic approach.

Middleton (1997) argues passionately for use of yield-line analysis for both slab and

beam-and-slab bridge decks and has produced a collapse mechanism analysis program called

Concrete Bridge Assessment (COBRAS). It uses graphics and 3D modelling techniques

which, it is claimed has the ability to analyse rigorously realistic configuration of loading,

bridge geometry, support fixity, and failure mechanism, without the need to derive the

mathematical expressions describing the interrelationship between those parameters. A

typical bridge assessment can be completed in a few minutes.

The program has been calibrated against published analytical solutions; results fromNLFE analysis. In almost all the methods the yield-line gave a conservative estimate of

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strength. The method clearly has high potential especially for short span bridges. For simply

supported short span bridges it is possible to choose set of probable failure mechanisms to

enable the work equation and to find the strength of bridge deck.

TYPICAL FAILURE MODES BY YIELD-LINE FOR A SIMPLY SUPPORTED SLAB

BRIDGES.

11.2.2.2 STRUT AND TIE ANALYSIS

Strut and tie analysis is commonly used for the analysis of the pile caps and

anchorages. It is also used for the analysis of diaphragms and deep beams. The principle is

based on establishing compressive struts of concrete and tensile ties of reinforcement.

The size of the compressive strut is dependent on allowable compressive stress for the

grade of concrete and the force carried. The method usually requires iterations to establish the

appropriate geometry of the strut and the reinforcement in the ties.

11.2.3 NON LINEAR FINITE ELEMNT ANALYSIS

NLFE programs are able to model the non-linear characteristics of a bridge deck

under the gradual load applied such as the change of stiffness as the concrete cracks; the non-

linear nature of the stress-strain curve for steel reinforcement, the non-linear and load-

displacement relationship that results when the deflection becomes large, in-plane force. In

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this sense they are very realistic form of analysis in that they seek to model the bridge

behaviour incrementally at every point in the load history right up to collapse. NLFE

programs are, however, very expensive to buy at the moment and require a high level of

expertise in order to use them effectively. They are also sensitive to the material properties

chosen and generate much output.

Henriques (1996) describes the use of NLFE program to model a two span twin box

girder bridge of concrete, but the results are nowhere are verified by the test data- as for

example measurement of deflection measurement under the load and are therefore unreliable.

Jackson (1996), on the other hand, used NLFE program to predict the behaviour of an in-fill

joist type bridge which was actually tested to destruction and he clearly explains the

limitations of the analysis. He concludes, that in a particular case, the predicted reserve

strength was justified in that it was conservative compared to the actual value, and therefore it

is probable that NLFE programs have a role to play in assessment. Jackson and Cope in 1990

carried out an assessment of two half-scale beam and slab decks using various methods

including NLFE analysis. The decks were then tested to failure and then the failure loads

were compared to those obtained from various methods. The conventional method based on

elastic theory and yield-line approach gave a conservative results. They found, however, that

not only did the NLFE analysis predict the failure load, but also the failure mode. They

conclude that the prediction methods which predict the correct failure load but the wrong

mode must be considered highly suspect.

Use of NLFE programs are likely to remain in the domain of research for some time

to come and in the mean time they should be used with caution and if possible backed up by

physical tests.

12.0 COMPARISON BETWEEN STRUCTURAL ANALYSIS FOR DESIGN AND

STRENGTH ASSESSMENT

Structural analysis for assessment is apparently similar to the structural analysis for

the design. However, there are important and fundamental differences between the two

approaches. These differences need t be appreciated, otherwise they can result in significant

waste of resources on unnecessarily sophisticated analysis. The results of analysis may result

in structures being strengthened or even declared as unsafe, even when they are satisfactory.

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In contrast to the design, the details of the structure being assessed are fixed.

Therefore it is necessary to choose an analysis which is appropriate to the structure. The

structure cannot be altered to suit the analytical results; the analysis has to be adjusted to suit

the structures.

When an analysis suggests that something is inadequate, its significance should

always be evaluated. It may be a real problem but, frequently, there are other analytical

methods available that can prove it is not. Even if this analysis is very expensive, it is still

likely to be cheaper than restoring to strengthening the structures.

There is no reason to use an analysis that is any more expensive than the minimum

required proving the structure adequate. If more sophisticated and expensive analysis are

used (compared with static load distribution) then there should be logical reason for the

choice.

A simple, non-linear or plastic analysis may fully satisfy the serviceability

requirements. Serviceability checks and inspections can be used to assess the potential risks

of durability problems arising during the remaining life of the structure.

13.0 CONCLUSIONS

Overall, the use of elastic analysis methods for assessing the ultimate load capacity of

concrete bridges may in many situations result in a significant under-estimate of strength. The

development of the COBRAS yield-line program provides a very powerful alternative tool

with which plastic collapse analyses of these bridges can be undertaken for a wide selection

of possible failure modes and assessment load cases. As an upper-bound approach, care must

be used in applying this technique however there is substantial theoretical and experimental

evidence to support its validity for concrete bridge decks in which sufficient ductility exists to

justify the assumptions inherent in yield-line theory.

REFERENCES

Strength assessment of bridge structures- By Santosh K. Singh and Ayan

Bhattacharya- Structural design engineers- Global design centre.

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Evolution of bridge performance data and assessments John M. Hooks

Bridge evaluation through non-destructive testing Azlan Adnan, Karim

Mirasa.

Sustainable concrete bridge assessmentJon Shave

Assessment and strengthening of structures Nirjhar Dhang

Concrete bridge assessment C. R. Middleton University of Cambridge, U.K.

Strategies for bridge assessment M. J. Baker, P. J. Dowling Imperial college

science and technology London.

strength assessing of bridges

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