strength evaluation of existing steel; concrete and masonry arch bridges

Chapter 14Bridge Design Manual - 2002 Strength Evaluation of Existing Steel; Concrete and Masonry Arch Bridges

Ethiopian Roads Authority 4-1

14 STRENGTH EVALUATION OF EXISTING STEEL, CONCRETE AND MASONRY

ARCH BRIDGES

14.1 INTRODUCTION

14.1.1 PURPOSE

These proposed guidelines establish a methodology for rating existing bridges. They aremainly based on AASHTO (Ref. 1). The guidelines address several shortcomings of existingevaluation procedures. The methodology is developed within a framework that provides fora systematic rating improvement in the evaluation process. Moreover, the methodologycan be used in conjunction with a wide range of engineering practices.

The aim of this chapter is to provide a comprehensive yet flexible methodology forevaluating existing bridges, which is consistent with today’s high standards of safety.

Regarding the strength of existing masonry and concrete arch bridges, refer to section 14.5.

14.1.2 SCOPE

The methodology presented utilizes Load and Resistance Factor Design (LRFD). Thisprocedure allows for combining probability theory, statistical data and engineering judgmentinto a rational decision making tool. In particular, the procedure allows the engineer to usesite specific information in a consistent manner to improve, if necessary, his judgment on thesafe rating level for a particular bridge. In addition, the format incorporates existingmethodology for considering local laws and regulations and methods of calculation.

A load and resistance factor approach was also chosen as the basis for strength evaluation ofexisting bridges as it conforms to the design methods for new bridges specified earlier in thismanual, while still allowing for a systematic consideration of the differences involved inbridge evaluation. This approach allows each variable to be addressed separately, analyzedin depth (if needed), and proportionally weighed in the overall rating process.

Conservative assumptions are made in each step of a strength design or checking procedureto safeguard against the worst possible conditions expected to occur during the lifetime of astructure. In other words, the probability of failure is made exceedingly small by providinglarge safety margins to cover the uncertainties in predicting load effects and resistance of abridge. Reliability principle utilizing site data have been used to evaluate the uncertaintiesand the safety levels or indices implicit in current designs.

The rating methodology and load and resistance factors have been developed to maintainconsistent safety levels for the above-mentioned uncertainties. Options for incorporating sitespecific traffic and loading data and higher levels of effort by the engineer are introducedsince these lead to a reduction in the overall uncertainty. The lower safety margin requiredmaintaining the same safety level means ratings that are more beneficial. At no stage is it

Chapter 14Strength Evaluation of Existing Steel; Concrete and Masonry Arch Bridges Bridge Design Manual - 2002

Page 14-2 Ethiopian Roads Authority

necessary for the evaluation engineer to use probabilistic methods. The necessaryreliability-based load and resistance factors have been tabulated for the evaluation.

Load and resistance factors were calculated from the coefficient of variation of actual loadeffects and resistances, the ratio of the mean value to nominally determined values (i.e., thebias) and the desired safety level. Therefore, as the evaluator obtains more data on thedistribution of actual load effects and resistances, more realistic load and resistance factorscan be utilized.

14.1.3 APPLICABILITY

This methodology is intended for evaluating almost all existing bridges. Steel spans includesimple and continuous girder bridges and trusses and floor systems. Concrete spansrecognized include slab, girder, T-beam and box beam bridges with short to medium spanlength. Prestressed beams although of recent vintage are also included herein.

14.2 NOTATIONS

Af = Axle factorAp = Centrifugal distribution factorADT = average daily trafficADTT = average daily truck trafficd = Arch barrel thicknessD = nominal dead load effectDi = Nominal dead load effect of element “i”FA = Centrifugal effect factorFb = Barrel factorFc = Condition factorFd = Depth factorFf = Fill factorFj = Joint factorFm = Material factorFmo = Mortar factorFp = Profile factorFsr = Span/rise factorFw = Width factorFy = nominal or specified yield stressh = Depth of fillI = live load impact factorI = “Impact Factor” used to approximate the dynamic effects of moving Legal Trucks.l = nominal traffic live load effectsKL = Proportion factor for longitudinal girdersL = Span of archL = nominal live load effectLj = Nominal traffic live load effects for load “j” other than the rating Legal Truck.LR = Nominal live load effects for the rating Legal Truck.


Ethiopian Roads Authority Page 14-3

m = total number of elements contributing to dead load to the structure.ME = Equivalent axle load for bending moment effectn = total number of live loadings contributing to the live load effects other than the

rating legal truck(s).PAL = Provisional axle loadingQk = Effect of load kR = resistanceR = Bending moment or shear without centrifugal effectsRc = Enhanced bending moment or shearRn = nominal strength or resistanceRF = rating factor (the portion of the rating Legal Truck allowed on the bridge)rc = Rise of arch barrel at crownrq = Rise of arch barrel at quarter pointsSE = Equivalent ax le load for shear force effectSL = Shear on longitudinal memberSU = Gross shear due to one lane of UDL (Uniform Distributed Load)γD = dead load factorγi

D = dead load factor for element “i”.γL = live load factorγj

L = live load factor for load “i” other than the rating Legal Truck.γLR = live load factor for the rating Legal Truck.φ = Resistance factor (Capacity reduction) to account for uncertainties in resistance due

to variations in dimensions, material properties, and theory.

14.3 STRENGTH EVALUATION OF BRIDGES

14.3.1 GENERAL

The procedure for rating existing bridges requires knowledge of the physical conditions ofthe bridge and the applied loadings. A safe level of rating presupposes that nominal strengthsshould be estimated from a detailed investigation of the structure’s physical condition andany continuing attempts to alleviate any signs of deterioration. Further knowledge of trafficconditions including signs of overweight vehicle combinations combined with accuratemethods of structural analysis should be used when necessary to estimate load effects.

The load and resistance factors (LRFD) that must be applied should rationally recognize thecorresponding uncertainties in making these judgments on strength, analysis and loading.The concepts of structural reliability are a means for consistently representing theseuncertainties and allowing bridge engineers to select proper load and resistance factors forrating specific bridges.

The evaluation of a structure is based on the simple principle that the available capacity ofa structure to carry loads must exceed the required capacity to support the applied loadings.To perform an evaluation, therefore, it is necessary to know something about the availablecapacity, the applied loading and the response of the structure to that loading. Knowledge



and information with respect to each of these items is never complete; and therefore,evaluation can never be done precisely.

To compensate for this lack of knowledge and information, engineers have used safetyfactors to insure that failure does not occur. The Load and Resistance Factor Design(LRFD) has been introduced in design and rating to provide more uniform safety. Themethod implicitly recognizes that dead load effects may require lower safety margins thancomparable live (truck) load effects due to their relative uncertainty. This probabilisticapproach to safety is logically extended in the load and resistance factor methods usedherein.

The rating check is done by comparing the factored load effects (both dead and live) withthe factored resistance at all critical sections. The output is a rating factor, whichdetermines the suitability of the given bridge for the loads under consideration. If the bridgerating is not acceptable, several options for a more detailed analysis are given. Each of theseoptions are associated with an increasing level of effort and shall be done if the ratingengineer warrants their use. An initial screening level, however, is provided for routineinvestigations.

Advantages of this method are:1. It provides uniformly consistent procedures for evaluating existing bridges.2. It permits suitable flexibility in making evaluations.3. It provides uniform levels of reliability developed from performance histories.4. It is based on extensive truck traffic and bridge response data.5. It permits introduction of site specific data into the evaluation in a rational and consistent

format.6. It permits different levels of effort that involve progressively more work; with

correspondingly greater rewards in terms of more beneficial ratings.7. It includes the same nominal dead and live load calculations and resistances as in the

design of new bridges.8. It allows distinction between evaluation of redundant and nonredundant components.

14.3.2 SAFE EVALUATION

The strength evaluation procedures presented herein are intended to recognize a balancebetween safety and economics. Detailed presentations of the theory and the calibration of theload and resistance factors contained herein are given in Chapter 2: General Requirementsand Chapter 12: Detail Design of Bridges and Structures. A single load rating will beproduced by these guidelines.

Evaluators will find options in these guidelines by which ratings can be improved byrecommendations for more frequent and detailed inspection and maintenance, improvedstructural analysis and especially control of heavy overweight vehicles.

These guidelines are intended to produce rating factors for routine evaluation and postingconsiderations. Evaluation of live load for issuance of permits may require load factorsdifferent from rating and shall also utilize the actual vehicle size, weight and configuration.



Each of the steps in the evaluation process shall be performed in any one of several ways.Therefore, the proposed guidelines are general enough to accommodate the practices ofdifferent engineers and/or agencies. The load and resistance factors presented in theguidelines were developed on the principle that the accuracy of an evaluation was dependent,in part, on the methods used to perform the evaluation.

For economic reasons, it is desirable to keep the evaluation effort to a minimum. If thecapacity of a bridge can be shown to be sufficient by making some approximations, there isno need to resort to an expensive evaluation procedure. On the other hand, if the sufficiencyof a bridge cannot be reliably established using a more approximate method, an engineermay wish to resort to a more sophisticated approach in order to demonstrate the sufficiencyof the bridge. Therefore, the evaluation process outlined in the guidelines is a cyclic processin which one or several of the steps shall be repeated.

The various options provided in the guidelines along with corresponding land/resistancefactors have been developed so as to maintain an adequate level of safety based oncalibration with existing performance experiences. The evaluation procedures presentedherein therefore provide a balance between safety and economics.

The single load rating value produced by these guidelines shall be greater than currentoperating ratings for well-maintained, non-deteriorated and redundant load path bridgeshaving reasonably well enforced traffic. It may fall, however, even below existing inventorylevels for heavily deteriorated bridges or those having non-redundant components andsubjected to heavy truck traffic. A gradation of ratings between these two extremes will beobtained depending on the condition of the bridge, type and volume of traffic, the quality ofinspection and the regularity of maintenance. Thus, a deficient bridge shall be made to ratesufficiently if certain preventive measures such as load control restriction, inspection, etc.are undertaken. A variety of options may exist and the engineer could choose one of themdepending on the economics of the situation and the amount of effort the engineer is willingto expend.

14.3.3 THE RATING EQUATION

The evaluation is carried out with a comparison of the factored live load effects and thefactored strength or resistance. The load factors are used to account for uncertainties in loadeffects due to uncertainties in analysis as well as load magnitudes. The dead load factorincludes normal variations in material dimensions and densities.

The live load factor accounts for uncertainties in expected maximum vehicle loading effect,impact and distribution of loads during a time period between inspection. The resistancefactor accounts for uncertainties in strength prediction theories, material properties anddeterioration influences over time periods between inspection. Furthermore, the load andresistance factors are adjusted to produce an overall safety margin which leads to anadequate level of safety considering all uncertainties described above.



The rating procedure is carried out for all strength checks (moment, shear, etc.) at allpotentially critical sections with the lowest value determining the rating factor for the entirespan. The rating equation to be used throughout the application of these guidelines is:

φRn = γDD + γL (RF) L (1 + I) (14.1)

or: (14.2)

Where: RF = rating factor (the portion of the rating Legal Truck allowed on the bridge)φ = resistance factorRn = nominal resistanceγD = dead load factorD = nominal dead load effectγL = live load factorl = nominal traffic live load effectsL = nominal live load effectI = live load impact factor

The rating factor is the ratio of the safe level of loading to the load produced by the nominalor standard vehicle. It shall be used in the consideration of posting levels and/or theconsideration and justifications for future repairs or replacement. In determining load andresistance factors for the rating equation, the following steps shall be carried out inevaluating a bridge span:

1) collection of information2) selection of nominal loadings and resistances3) distribution of loads4) selection of load and resistance factors5) calculation of rating factors

A flowchart for the rating procedure is also provided in Figure 14-1. The evaluator/designershould note that potential improvement in the rating factor may came from selecting optionsin each step. These generally provide a less conservative factor provided additionalevaluation effort is performed and no unsatisfactory information is uncovered.

The basic structural engineering equation states that the resistance of a structure must equalor exceed the demand placed on it by loads. Stated mathematically:

R ≥ Σ Qk (14.3)

Where: R = resistanceQk = effect of load k

The solution of this simple equation encompasses the whole art and science of structuralengineering including the disciplines of strength of materials, structural analysis and load

)1(* IL

DRRF

L

Dn

+−=

γγφ



determination. This equation applies to design as well as evaluation. In structural evaluation,the objective is to determine the maximum allowable live load. In the case of bridgeevaluation, this usually means the maximum vehicle weight.

Any rational and tractable approach to the analytical solution of the basic structuralengineering equation requires that the modes of failure be identified to establish theresistance. The location, types and extent of the critical failure modes must be determined.The checking equation must be solved for each of these potential failure checking modes.

Since neither resistance nor the load effect can be established with certainty, safety factorsmust be introduced that give adequate assurance that the limit states are not exceeded. Thisshall be done by stating the equation in a load and resistance factor (LRFD) format.

The basic rating equation used in the guidelines is simply a special form of the basicstructural engineering equation with load and resistance factors introduced to account foruncertainties that apply to the bridge evaluation problem. It is written as follows:

(14.4)

Where: RF = rating factor (the portion of the rating Legal Truck allowed on the bridge)φ = resistance factorm = number of elements included in the dead loadRn = nominal resistancen = number of live loads other than the rating vehicleγi

D = dead load factor for element “i”Di = nominal dead load effect of element “i”γj

L = live load factor for live load “j” other than the rating vehicle(s)Lj = nominal traffic live load effects for load “j” other than the rating vehicle(s)γLR = live load factor for rating Legal TruckLR = nominal live load effect for the rating Legal TruckI = live load impact factor

The maximum permitted traffic live load effect will be the total resistance minus the effectof loadings other than the rating Legal Truck. This will include dead loads, non-vehicularlive loads, and, in the case of unsupervised permit loading, the vehicular live load and theimpact of normal traffic that could mix with the rating Legal Truck.

)1(

)1(*1 1

IL

ILDRn

RFR

LR

i i

jjn

iim LD

+

+−−=

� �= =

γ

γγφ



Start

Collect information(1) Deck condition(2) Structural Condition(3) Traffic condition

Calculate dead loads(Table 14-1)

Select live loads andImpact factor

(Figure 14-2 to 14-4 and Table 14-2)

Determine nominal resistance(Table 14-3)

Calculate load effects(1) Dead load(2) Live load

(Chapter 3)

Select resistance factor(Figure 14-6 and Table 14-6)

Select load factor (Table 7-5)(1) Dead load(2) Live load

Calculate rating factor R.F.

The safety level is acceptable

Conduct a moreDetailed

Analysis warrantedby the Engineer

Post or Modify

No

Yes

Figure 14-1 Flow Chart for Rating Procedure

Is safety levelacceptable?

No

Is R.F. < 1Yes



Collection of Information

Before the load rating of a specific bridge can be conducted, a certain amount of informationhas to be gathered. The extent to which the engineer is required to collect information willhave a direct influence on the load rating of the bridge due to the selection of the propercategory for the load and resistance factors.

This task shall be the same as the provisions in the existing section 4.9: Site Investigation:Checklist of Site Investigation except that the following items should be noted since they canhave an influence on the selection of load and resistance factors.

1. Deck condition – The impact factors in section 3.8: Live Loads are deliberately selectedto be conservative with respect to most conditions. Field tests have shown that the singlemost important factor affecting impact is roadway roughness and any bumps, sags, orother discontinuities which may initiate or amplify dynamic response to truck passages.Any of these surface factors should be noted during a bridge inspection.

2. Structural Condition - Signs of recent deterioration in structural members, which may gounchecked and increase the likelihood of further section capacity loss before the nextcycle of inspection and rating should be noted. Conversely, maintenance efforts tomitigate such deterioration should also be noted. An allowance for structuraldeterioration should note whether this is either an expected or conservative estimationsince further deterioration may increase the uncertainty regarding reliable sectionproperties and strength during the next inspection interval.

3. Traffic Condition - The expected loading during the inspection internal is affected bythe truck traffic at the site. In the best instance, data will be available from traffic surveysincluding objective truck weight operations. Alternatively, advice should be sought fromthe traffic division regarding truck traffic volume, composition, permit activities,overload sources, and degree of enforcement.

Selection of Nominal Loading and Resistances

Loads consist of concentrated or distributed forces that are applied directly to the bridge orresult from deformations or the constraint of deformations. For bridge evaluations, the mostimportant loads are dead load and vehicular live load plus its accompanying dynamic effects,since each of these loadings induce high superstructure stresses. Loadings other than deadload and traffic live load usually do not result in significant bending or shear in thesuperstructure. Since the critical mode of failure for traffic live load almost always occurs inthe superstructure, other types of loads will seldom affect the live load capacity of thebridge. When other combinations of loads can affect the capacity of the bridge such as whensubstructure components can fail due to traffic live loading, the Chapter 3: LoadRequirements load factors for design shall be used.



Dead Loads

The dead load shall be estimated from data available from the inspection at the time ofanalysis. The dead load factor accounts for normal variations of material densities anddimensions. Nominal dimensions and densities shall be used for calculating dead loadeffects. For overlays, either cores shall be used to establish the true thickness or an additionalallowance of 20% should be placed on the nominal overlay thickness indicated at the time ofanalysis. The recommended unit weights of materials to be used in computing the dead loadshould be as in Table 14-1:

Table 14-1 Unit Weights of Materials

MATERIAL FORCE EFFECT [kN/m3]Asphalt surfacing 22.5Concrete, plain or reinforced (normal weight) 24.0Steel 79.0Cast iron 72.0Timber (treated or untreated) 8.0Earth (compacted), sand gravel or ballast 18.0

The dead load of the structure is computed in accordance with the conditions existing at thetime of the analysis.

Dead load can usually be determined more accurately than any other type of loading. Onemajor source of error is failure to consider some of the elements that will contribute to deadload. Some items that are often overlooked are:• Wearing surfaces• Railings and Utilities• Structure modifications not shown on plans

Other items that can affect the calculation of dead load are dimensional variations in theconcrete section and variations in the unit weight of material.

The prescribed dead load factor recognizes the uncertainties in the nominal dimensions andanalysis of dead load effects. Overlay thicknesses are a source of greater uncertainty in thedead load so they are assigned a 20% higher load factor unless cores or more detailedmeasurements are made.

Live Loads

The guidelines specify the number of vehicles to be considered on the bridge at any onetime. These numbers are based on an estimate of the maximum likely number of vehiclesunder typical traffic situations. When unusual conditions exist, adjustments to the specifiednumber of vehicles should be made.



Highway vehicles come in a wide variety of sizes and configurations. No single vehicle orload model can accurately reflect the effects of all of these vehicles. The variation willusually be greater than the variation in dead load effect. To minimize this difference, it isnecessary to select a rating Legal Truck with axle spacing and relative axle weights similarto actual vehicles. Three Legal Trucks shown in Figure 14-2 to 14-4 are recommendedas evaluation vehicles. These vehicles, together with the prescribed live load factors, give arealistic estimate of the maximum live load effects of a variety of heavy trucks in actualtraffic.

The moving loads to be applied on the deck for calculating maximum nominal live loadingeffects shall be the three Legal Trucks. The spacing and axle weights chosen for thesevehicle types were selected from actual trucks. It is believed that these typical vehiclescorrespond better to existing traffic and will provide more uniform reliability than the oldstandard AASHTO H or HS design trucks. Hence, the latter are not recommended for bridgeposting purposes.

In computing load effects, one Legal Truck shall be considered present in each lane. Thepositioning of the vehicle in each lane shall be according to Chapter 3: Load Requirements.It is unnecessary to place more than one vehicle in a lane since the load factors shown belowhave been modeled for this possibility. These load factors shall be considered applicable forspans up to 60m.

For longer spans, a lane loading is specified in the evaluation. Reduction factors for liveloading of more than two traffic lanes are provided. These rationally account for the lowerpossibility of such occurrences.

INDICATED CONCENTRATION LOADSARE AXLE LOADS IN KN

CG = CENTER OF GRAVITY

ALL DIMENSIONS IN METER

Figure 14-2 Truck Type 3 Unit Weight = 227 kN



Figure 14-3 Truck Type 3-2 Unit Weight = 325 kN

Figure 14-4 Truck Type 3-3 Unit Weight = 364 kN

Figure 14-5 The Legal Lane Loading (mainly for large spans)

For longer spans, the Legal Lane Loading given in Figure 14-5 will govern the evaluation(up to 90 m). This is a combination of a vehicle load and a uniformly distributed load. For allspan lengths where the rating factor is less than one, it shall be necessary to place more than



one vehicle in each lane. In lieu of this, the evaluator should check the lane loading for allspan lengths together with the rating Legal Truck as shown in Figure 14-5. Where maximumload effects in any member are produced by loading a number of traffic lanessimultaneously, reduction factors as given in Table 14-8 should be applied.

In checking special permits, the actual vehicle weights and dimensions shall be used. If thenumber of such permits in one year are frequent, then it shall be assumed that two lanes areoccupied by such a vehicle. Otherwise, standard vehicles shall be placed in the other lanes.When the engineer determines that conditions of traffic movement and volume warrant it,the standard vehicles shall be eliminated. Upon special investigation, the load factor for acontrolled permit use is reduced below the value taken for ordinary traffic conditions.

Since overload permissible vehicles typically have very different axle configurations, it isvery important that this be considered when issuing permits.

Judgment must also be exercised concerning sidewalk loadings. The likelihood of themaximum sidewalk loading is small. A unit loading for the sidewalk for the purposes ofload limit evaluation will generally be less than the design unit loading.

The probable maximum sidewalk loadings should be used in calculations for safe loadcapacity ratings. This loading will vary from bridge to bridge, depending generally upon itslocation. Because of this variation, the Engineer must use his judgment to make the finaldetermination of the unit loadings to be used. This loading will not exceed the designsidewalk loading given in Chapter 3: Load Requirements.

Impact

An impact allowance shall be added to the static loads used for rating as shown in Equation14.1. Impact values in Chapter 3: Load Requirements reflect conservative conditions thatmay possibly prevail under certain circumstances. Under an enforced speed restriction,impacts shall be reduced.

Impact loads are taken to be primarily due to the roughness or unevenness of the roadsurface, especially the approach spans. Three values of impact factors are provided bycorrelating the roughness of the surface to the deck conditions survey values. Thisinformation is more likely known during evaluation than in the original design.

For smooth approach and deck conditions, the impact shall be taken as 0.10. For a roughsurface with bumps, a value of 0.20 should be used. Under extreme adverse conditions ofhigh speed, spans less than 12m. and highly distressed pavement and approach conditions, avalue of 0.30 should be taken. For span ≤ 12.0 m, where the measured deflection exceeds1/90 of the span, 0.10 should be added to these values. See Table 14-2.

If such a judgment cannot be made, refer to the bridge inspection report and relate impact tothe condition of the wearing surface.


-14 Ethiopian Roads Authority

Table 14-2 Condition of Wearing Surface and Impact Value

WEARING SURFACE IMPACT1 - Good condition No repair required 0.12 - Fair condition Minor deficiency, item still functioning as

designed0.1

3 - Poor condition Major deficiency, item in need of repair tocontinue

0.2

4 - Critical condition Item no longer functioning as designed 0.3

Resistances.

Nominal component strengths shall be the same values contained in the load factor sectionsof Chapter 3: Load Requirements. Nominal strength calculations shall take intoconsideration the observable effects of deterioration, such as loss of concrete or steel cross-sectional area, loss of composite action or corrosion.

Concrete: The strength of sound concrete shall be assumed to be equal to either the valuestaken from the plans and specifications or the average of construction test values. Whenthese values are not available, the ultimate stress of sound concrete shall be assumed to be 25MPa. A reduced ultimate strength shall be assumed (no less than 15 MPa, however) forunsound or deteriorated concrete unless evidence to the contrary is gained by field-testing.

Reinforcing Steel: The area of tension steel to be used in computing the ultimate flexuralstrength of reinforced concrete members shall not exceed that available in the section or 75percent of the steel reinforcement required for a balanced condition. The steel yield stressesto be used for various types of reinforcing steel are given below.

Reinforcing Steel Yield Stress Fy (MPa)Unknown steel (prior to 1954) 228Structural Grade 248Intermediate Grade 300 and unknown after 1954 (former Grade 40) 276

Hard Grade (former Grade 50) 314Grade 420 (former Grade 60) 614Grade 520 (former Grade 75) 517

Table 14-3 Reinforcing Steel Yield Stresses

The determination of structural resistance is one of the primary tasks in the evaluationprocess. In a load and resistance design (LRFD - also known as limit state) approach it isnecessary to define the condition at which resistance will be determined. These shouldprovide for similar structural performance regardless of the material or structure type.



These limit states should have a very low probability of occurrence because they can lead toloss of life as well as to major financial losses. They include:• Loss of equilibrium of all - or part of - the structure considered as a rigid body (e.g.,

overturning, sliding, uplift, etc.);• Loss of load-bearing capacity of members due to insufficient material strength, buckling,

fatigue, fire, corrosion, or deterioration;• Overall instability of the structure (e.g., P-delta effect, wind flutter, seismic motions,

etc.);• Very large deformation (e.g., transformation into a mechanism).

Determination of the true safety limit state involves very complicated and difficultanalytical procedures. In most cases, the use of these procedures for routine evaluation ofbridges is not economically feasible. The ultimate member capacity shall be a lower boundof the ultimate capacity in shear or in flexure. Different methods for considering theobservable effects of deterioration were studied in developing the guidelines. The mostreliable method available still appears to be a reduction in the nominal resistance based onmeasured or estimated losses in cross-sectional area and/or material strengths. An alternateapproach is to calculate resistance based on plan dimensions and use a smaller capacityreduction factor.

Nominal resistances for members in the proposed guidelines are based on the load factorsection, Chapter 3: Load Requirements. This resistance depends on both the currentdimensions of the section and the nominal material strength. Specifications for both thesefactors have been provided. Options exist for incorporating data on structural conditionsobtained from the site. Careful estimation of losses and deterioration are awarded a higherresistance factor. Similar gains are also given for vigorous maintenance and inspectionschedules, which may prevent further deterioration during a normal inspection interval.Options also exist for obtaining more precise material strength through tests.

Structural Steel

Nominal unit stresses must depend on the type of steel used in the structural member. Whentests are performed to assess yield stress, the mean values shall be reduced by 10% toproduce nominal values for strength calculations. Nominal values shall be nominal strengthcomputed without any resistance factor applied.

Distribution of Loads

The fraction of vehicle load effect transferred to a single member shall be selected inaccordance with Chapter 3: Load Requirements. These values represent a possiblecombination of adverse circumstances. The option exists to substitute field measured values,analytically calculated values or those determined from advanced structural analysis methodsutilizing the properties of the existing span(s). Loadings shall be placed in positions causingthe maximum response. Further, if such a measurement or analysis is made and the expecteddistribution value is obtained, then this shall be adjusted by the factors shown in Table 14-4.



The latter are needed to adjust for the expected bias in distribution factors for differentmaterial types.

Correction FactorDistributionof Loads

Steel Prestressed Concrete

1 AASHTO Distribution, Chapter 13 1.00 1.00 1.00

2 Tabulated analysis with simplified assumptions** 1.10 1.05 0.95

3 Refined analysis: finite elements, orthotropicplate, grillage analogy

1.07 1.03 0.90

4 Field measurements 1.03 1.01 0.90

Actual girder distribution shall be multiplied by the appropriate correction factors to obtainthe girder distribution for rating.

* Correction factors are applied if average or expected values are used for R.F. from analysis or measurements.The correction factor shall be used to increase the load factor taken from Table 14-5.

** These correction factors reflect the bias in present Vol. I distribution factors for each material type.

Table 14-4 Correction Factor for Analysis*

Lateral distribution refers to the fraction of the live load carried by the member underconsideration. Methods in Chapter 3: Load Requirements shall be followed. Options existfor using tabulated values, more refined analysis (e.g. finite elements) and fieldmeasurements. Each of these options involves a greater level of effort and more accuracy, soadjustments to the basic live load factors are provided. These adjustments implicitlyrecognize that more refined analysis may in some instances remove the implicitconservativeness present in some simplified distribution formulas and are therefore treatedaccordingly.

Selection of Load and Resistance Factors

The statistics of the dead load, live load and resistances have been determined from existingdata. Based on this data, the safety implicit in current designs has been determined. The loadand resistance factors provided ensures that this acceptable level of safety is achieved orexceeded.

Load Factors

The load factors shall be taken from Table 14-5. These are intended to represent conditionsexisting at the time this specification is written based on field data obtained from a variety oflocations using weight-in-motion and other data gathering methods. The live load factoraccounts for the likelihood of extreme loads side-by-side and following in the same lane andthe possibility of overloaded vehicles. Since one aim of this chapter is to protect theinvestment in the bridge structure, the live load factors do recognize the presence of



overweight trucks on many highways. An option to reflect effective overload enforcement iscontained herein with a reduced live load factor. The presence of illegal loads has also beennoted, and if such vehicles are present in large numbers at the site, the higher load factorsmay lead to unacceptable ratings and enforcement efforts should be instituted.

Loading Load Factor

Dead Load γD = 1.2

Allow an additional allowance of 20% on overlay thickness if nominal thicknessesare used. No allowance is needed when measurements are made for thickness.

Live Load Category

1 Low volume roadways (ADTT less than 1000), reasonableenforcement and apparent control of overloads

γD = 1.30

2 Heavy volume roadways (ADTT greater than 1000), reasonableenforcement and apparent control of overloads (not common inEthiopia)

γL = 1.45

3 Low volume roadways (ADTT less than 1000), significant sources ofoverloads without effective enforcement (common in Ethiopia)

γL = 1.65

4 Heavy volume roadways (ADTT greater than 1000), significantsources of overloads without effective enforcement

γL = 1.80

If unavailable from traffic data, estimates for ADTT shall be made from ADT as follows: urban areas, ADTT =25% of ADT; rural areas, ADTT - 50% of ADT. In the absence of accurate data on overloads, it shall beassumed that 30% of the trucks in Ethiopia exceed the local legal gross weigh limits.

Table 14-5 Load Factors

When the Rating Factor (R.F.) is less than 1.0, the loads are to be restricted. In suchinstances, consideration should be given to truck weight surveys and vigorous enforcementprograms. If there is a reason to believe that truck posting signs are being ignored thenconsideration should be given to further raising the live load factor.

Dead load factors are used to account for variations in dimensions, unit weights and methodsof calculating dead load effect. The variation in the dead load of different components willdepend on the accuracy with which the components can be manufactured and/or measured.Factory produced girders cast in steel forms obviously have less variation than an asphaltoverlay placed on the bridge deck. The higher dead load factor for asphalt recognizes thegreater uncertainty in overlay thickness.

Live load factors have been provided to account for the large uncertainty of the maximumlive load effects on a structure over a period of time. A large amount of filed data has beenmodeled to estimate the maximum live load effect together with its uncertainty. Based onthis data, degree of enforcement, volume and type of traffic are isolated as the major factorsinfluencing the live load effect. The live load factors have been derived from this data for



bridges with a single lane, two lanes and three and four lanes. Instead of providing differentsets of load factors for different numbers of lanes, only one set of load factors are providedwith corresponding reduction factors for other cases.

Three categories of live load are provided in Table 14-5 with varying volumes and degreesof enforcement, each with its corresponding live load factor. Site truck traffic data recordedby the engineer may also be included.

Resistance Factors

A capacity reduction factor (φ) is included in the basic rating equation to account forvariation in the calculated resistance. It takes into consideration the dimensional variations ofthe structure, differences in material properties, current condition and future deterioration,and the inaccuracies in the theory for calculating resistance.

The resistance factors or capacity reduction factors in Chapter 3: Load Requirements areintended for new components with current methods of high quality control. The nominal(unfactored) strengths to be used for evaluation represent an estimate of strength using datapertaining to member properties and conditions at the time of inspection. The resistancefactor shall consider both the uncertainties in estimating these member properties and alsoany bias or conservativeness deliberately introduced into these estimates. Because furtherchanges may occur to the section during the inspection interval, there is some dependence ofthese properties on the quality of maintenance. Also, the level and detail of inspection isimportant since it may reveal actual properties to be used in section calculations.

The resistance factors for members in good condition are shown in Table 14-6, section I. Theinfluence of deterioration, inspection and maintenance are given in section II, III and IV ofthis table. A table of resistance factors for all combinations of conditions encountered isgiven in Table 14-7. A flow chart for obtaining the resistance factors is also presented inFigure 14-6.

A basic set of resistance factors is provided. The reliability levels are calibrated to producedifferent resistance factors for redundant and non-redundant spans with the latter havinglower (more conservative) factors. The resistance factors can be further modified dependingon the amount of deterioration and type of inspection and maintenance. Options exist forconducting detailed measurements of strength losses. Also included are benefits for vigorousmaintenance schedules. This allows the evaluation to be flexible enough and also covers alarge range of types and conditions of members that shall be encountered.

Calculation of Rating Factors (RF)

The rating factor is to be calculated from Equation 14.1. If it exceeds 1.0, the span issatisfactory for the legal loads in Ethiopia. In the present Bridge Design Specifications,there is only one single rating value (eliminating the operating and inventory levels) whichdetermines the allowable loads.



Figure 14-6 Flowchart for Selecting Resistance Factors φ

START

CheckRedundancy

φ = 0.95 steel P/Sφ = 0.90 R.C.

φ = 0.80

AnyDeterioration ?

φ = φ - 0.1

How good isinspection ?

φ = φ + 0.05

φ = φ - 0.0

Type ofmaintenance

φ = φ - 0.05

φ = φ + 0.05

φ = φ - 0.2

isφ > 0.95 ?

φ = 0.95

φ

Yes

NoVigorous

Intermittent

Careful

Estimated

Heavy

Some

None

Yes

No



I Resistance Factors - Good conditionNominal resistance equations are to be those indicated in Chapter 3: LoadRequirements. Resistance (capacity reduction) factors are to be applied to the followingfor the case where members are in good condition. Redundant * Steel Members: φ =0.95; Nonredundant Steel Members: φ = 0.80; Prestressed concrete beams: φ = 0.95;Reinforced concrete beams: φ = 0.90;

II Influence of Deterioration

1. Where field inspection and condition survey reports indicate no deterioration, theprovisions of this section should not be used.

2. Where field inspection and condition survey reports indicate slight deterioration withsome possible loss of section, the resistance factor values above shall be decreased by0.1.

3 Where field inspection and condition surveys report significant deterioration andheavy section loss, the resistance factor values shall be reduced by 0.2.

4 If such information is not available then bridge records shall be used. Reduce theresistance factor values by 0.1 for superstructure condition of 5 or 6. Reduce theresistance factor values by 0.2 for a superstructure condition of 4 or less. If thesereductions are made then the next two sections should be omitted.

III Inspection*

1 Where field inspection and condition survey reports indicate no deterioration, theprovisions of this section should not be used.

2 Where section losses have been carefully estimated in the calculation of remainingsection areas the resistance factors shall be increased by 0.05.

3 Where material yield stress has been estimated by physical testing, a mean value of0.90 shall be used for calculating strength together with the resistance factor containedin the design rules.

IV Maintenance**1 Where maintenance activity is vigorous and likely to correct deficiencies which maylead to further section loss, increase φ by 0.05.2 Where maintenance activity is intermittent and may not correct defects that have leadto section loss, decrease φ by 0.05.

*Examples of redundant members include parallel stringers (three or more), parallel eye bars(four or more). Example of nonredundant component includes two-girder system(s) and trusseswith single members.** In no instance shall φ be taken to exceed 0.95.

Table 14-6 Resistance Factors vs. Condition



Redundancy Inspection MaintenanceSuper-structureCondition Yes No Careful Estimated Vigorous Intermittent

Steel,P/S

Concrete

ReinforcedConcrete

xxxx

xx

xx

x

xx

x

0.950.900.950.90

0.950.850.950.85Good or Fair

xxxx

xx

xx

x

xx

x

0.850.750.850.75

0.800.700.800.70

xxxx

xx

xx

x

xx

x

0.950.850.900.80

0.900.800.850.75Deteriorated

xxxx

xx

xx

x

xx

x

0.800.700.750.65

0.800.700.750.65

xxxx

xx

xx

x

xx

x

0.850.750.800.70

0.800.700.750.65Heavily

Deteriorated xxxx

xx

xx

x

xx

x

0.700.600.650.55

0.700.600.650.55

Note : For ratings using data obtained from plans only, the capacity reduction factor should be calculated basedon judgment of the engineer supplemented by any additional information obtained.

Table 14-7 Resistance Factors φ for All Conditions

The load and resistance factors have been calibrated to provide adequate safety under theinspection, maintenance, analysis, redundancy, and loading conditions cited. Theseprovisions have the capability for evaluations to be improved by utilizing options related tomore intensive inspection and maintenance or control of heavy overloads.

The rating factors obtained herein may also safely be applied to permit loadings. In someinstances where a permit might otherwise be rejected, the live load factors contained hereinshall be reduced to reflect known weight conditions associated with the permit vehicle. Thisreduction in load factor may depend on the degree of control of the permit and the number of



permits that shall be issued. Fatigue life should be a consideration in the issuance ofoverload permits (Ref. 2).

Number of Lanes Reduction Factor

One or two lanesThree lanesFour lanes

1.00.80.7

Table 14-8 Reduction Factors for Live Load

14.4 NUMERICAL EXAMPLES

As an example, an existing reinforced concrete bridge and a steel bridge are rated by theproposed procedures.

Example 1 – Reinforced Concrete

Resistance: Mu = Asfy (d – a/2)fy = 225 Mpa Table 14-3 fc = 21 MPad = 670 mm a = 29 mmAs = 4440 mm2 Mu = 670 kNm

Dead load effect: Span = 7,930 mmAsphalt = 45 kNm Other = 124 kNm

Live load effect: I = 1.1 (assuming smooth deck surface)

S = 2,000 mm g = 2000 = 1.091830

MLL = 254 (1.09) (1.1) = 152 kNm (Legal Truck No ‘3’)2

Proposed procedure: φ = 0.95 (good condition, vigorous maintenance)

R.F. = (0.95) (670) – (1.2) (124) – (1.44) (45) = 2.79γL (152) γL

Assuming enforced, heavy volume traffic: γL = 1.45 and R.F. = 1.92

Existing ratings : I = 1 + 50 ≤ 1.3 = 1.326 + 125

MLL = 254 (1.09) (1.3) = 180 kNm2



Operating rating = (0.9) (670) – (1.3) (124 + 45) = 1.64(1.3) (180)

Inventory rating 0.6 x 1.64 = 0.99 Proposed rating = 1.92 (Legal Truck No.‘3’)

Remarks: the proposed rating is higher than existing rating for traffic category 2 (thecalibration category) but will be lower than existing operating ratings for heavier trafficcategories. For a deteriorated section (say 10% loss in strength) and heavy traffic, theproposed rating can fall to existing inventory levels. See below:

φ = 0.80 (for deteriorated section)Mu = 670 kNmγL = 1.80 (unreinforced, heavy volume traffic)

RF = (0.80) (670) – (1.2) (124) – (1.44) (45) = 0.99(1.80) (180)

Example 2 Steel Floor beam of a thru truss

Resistance: Rn = 363 kNmφ = 0.85 (non-redundant; vigorous maintenance)

Dead load effect: Asphalt = 56 kNm, Remaining = 35 kNm

Live load effect: Impact = 1.1 (smooth surface and approaches)Live load effect = 161 kNm (Legal Truck No ‘3’)

Proposed procedure: Assuming enforced, light volume traffic, γL = 1.3

RF = (0.85) (363) – (1.2) (56) – (1.44) (35) = 0.91(1.30) (161)

Existing ratings: Impact = 1.3

Operating R.F. = 363 – 1.3 (56 + 35) = 0.99(1.3) (1.3) (146)

Inventory R.F. = 0.60

Remarks: The proposed procedure gives lower rating factors than existing operating ratingsbecause of the non-redundancy. However, this rating factor is higher than current inventoryratings.



14.5 MASONRY ARCH BRIDGE RATING

14.5.1 GENERAL

This subchapter is to be used in the assessment of highway arch bridges. It covers certaintypes of structures or structural components where firm criteria cannot be given but wherethe assessment of structural adequacy involves the exercise of engineering judgment. It alsocontains details of alternative simple methods of load distribution and arch assessment that,while being conservative, are nevertheless adequate for assessment purposes. Finally it givesadvice on ways of remedying the various defects that are found in different types ofstructure. Although this subchapter is advisory in nature, the principles and methods givenshall be deemed to satisfy relevant criteria.

14.5.2 SCOPE

This subchapter provides a simple method of load distribution and an empirical method anda simple computerized method of arch assessment. It covers the assessment of structureswhich cannot be treated by normal calculation methods, and the maintenance of the variousdifferent types of structure. Each of these items is discussed more fully in the followingparagraphs.

This subchapter should be used forthwith for assessments of load carrying capacity of allroad bridges and other arch structures in Ethiopia.

Load Distribution

Graphs of load distribution factors are given for estimating the loads carried by internal andexternal girders of decks composed of longitudinal beams with certain specified forms ofdeck construction between them. The factors are only intended for use with the type ofloading specified Chapter 3: Load Requirements, but can be used for determining bothbending moments and shearing forces.

Equivalent axle loads are given to enable the direct determination of bending moments andshearing forces in internal and external girders of decks composed of transverse beams withcertain specified forms of deck construction between them. The use of these simple methodsis both quick and simple and while they are believed to give conservative results their use isrecommended where applicable before more sophisticated and accurate methods are tried.

Modified MEXE Method of Arch Assessment

The modified MEXE method for arch assessment given in this subchapter is acomprehensive method for determining the carrying capacity of single span stone andmasonry arches in terms of allowable axle weights. The method as such is concerned solelywith the strength of the arch barrel and takes account of the materials, various defects andgeometric proportions which affect the strength of the arch. Factors are also given to takeaccount of the effects of multiple axles.



Substructures, Foundations and Retaining Walls

Advice is given for qualitative assessment of dry-stone walls, retaining walls, spandrel wallsof arches, sub-structures and foundations which cannot be assessed by mathematical meansbecause of the number of unknown parameters involved and their complex behaviour. Theadvice draws the attention of the engineer to the various defects likely to be found in themand comments on their structural significance. However, ultimately a satisfactory assessmentof such structures depends upon the correct interpretations of the physical observations andthe exercise of engineering judgement supported by local knowledge.

Maintenance

Many structures that have been damaged or have deteriorated in various ways can berestored to their original load carrying capacity by carrying out fairly straightforwardmaintenance. Advice is given on the importance of the various defects and the remedialmeasures that can be taken to alleviate them. All types of structure within the scope of thissubchapter are considered for this purpose.

14.5.3 RATING OF MASONRY ARCH BRIDGES BY THE MODIFIED MEXE METHOD

Scope

This section deals with the assessment of the strength of the ARCH BARREL ONLY. Thestrength of the bridge shall be affected by the strength of the spandrel walls, wingwalls,foundations etc. These items are dealt with in later sections of this subchapter. The modifiedMEXE shall be used to estimate the carrying capacity of arches spanning up to 18m, but forspans over 12m it becomes increasingly conservative compared to other methods. Themethod should not be used where the arch is flat or appreciably deformed.

ApSpanLongitudinal MemberEdge Girders Only

Transverse MemberSupported by ParapetGirders

Up to and including 6m 1.0 0.9Over 6m and up to andincluding 9m

0.9

Over 9m and up to andincluding 12 m

0.8

Over 12m and up to andincluding 15m

0.7

Centrifugal effect shallbe neglected

Table 14-9: Centrifugal Distribution Factor Ap



Method of Assessment

The assessment of the arch barrel (adapted from Ref. 4), is based on the results of pastexperience. It has been found to give satisfactory results for the range of vehicles present;but its extrapolated use for heavier vehicles, or for spans greater than 18m should be treatedwith caution. It is to be applied primarily to single span arches.

The initial assessment is in terms of a maximum allowable axle load on an axle forming partof a double axle truck. Factors are given in later section Application for converting this resultto other axle configurations and for situations where axle 'lift-off' may occur on the axle of amultiple axle truck.

Theory

The long-term strength of a stone or masonry arch is almost impossible to calculateaccurately and recourse has, therefore, been made to an empirical formula based on the archdimensions. The arch is first assumed parabolic in shape with span/rise ratio of 4, soundlybuilt in good quality stonework, with well pointed joints, to be free from cracks, and to haveadequate abutments.

For such an idealized arch, a provisional assessment is obtained from a nomogram (Figure14-7) or from the formula given in 14.7. This provisional assessment is then modified byfactors which allow for the way in which the actual arch differs from the ideal.

Survey of Arch

The arch should be inspected in accordance with provisions mentioned earlier in this chapter,and the following dimensions measured as shown in Figure 14-8:i. The span ..........................................................................................................L (m)

(in the case of skew spans, measure L parallel to the principal axis of the arch)ii. The rise of the arch barrel at the crown ...........................................................rc (m)iii. The rise of the arch barrel at the quarter points ...............................................rq (m)iv. The thickness of the arch barrel adjacent to the keystone (see following text) d (m)v. The average depth of fill, at the quarter points of the transverse road profile, between

the road surface and the arch barrel at the crown, including road surfacing... h (m)

The following information will also be required to derive the various modifying factors:• Type of material used for the arch barrel• Types of construction of the barrel i.e. are the stones laid in courses or laid at random?• Condition of materials in the barrel, i.e. is there a lot of spalling and are the stones sound

or are they deteriorating due to weathering'?• Deformation of the arch barrel from its original shape• Positions of dropped stones and the amount of drop• Width, length, number and positions of cracks• Type of filling above the arch and its condition• Position and size of services• Width of mortar joints• Depth of mortar missing from joints• Condition of joint mortar



Figure 14-7: Nomogram for Determining the Provisional Axle Loading of MasonryArch Bridges before Factoring



The appropriate measurements should be taken so that the arch barrel thickness shall beadjusted to allow for missing mortar (see Table 14-14) and to allow or any services laidthrough the arch barrel.

Figure 14-8: Arch Dimensions

Radial displacement of individual stones, especially near the crown when there is littlecover, should be particularly noted. Displacement shall be due to uneven masonry projectingabove the barrel and being subjected to concentrated loads or a hard spot such as a pipeflange bearing directly on the arch. The damage is usually localized and not serious if dealtwith before it has progressed too far. If, however, there are a number of stones displaced,then this should be taken into account, and the thickness of the arch barrel adjustedaccordingly.

Note should be taken of any evidence of separation of the arch rings, particularly with regardto any additional rings which have been constructed in later years, and due account shouldbe taken in the value assumed for the arch barrel thickness.

Provisional Assessment

The provisional axle loading PAL is obtained by reference to the nomogram in Figure 14-7.Mark the arch span L on Column A and the total crown thickness (d + h) (barrel and fill) onColumn B. Line through these points to Column C, and read off the provisional axle loadingassessment in tonnes. Alternatively, the provisional axle loading shall be obtained bysubstituting the values of (d + h) and L in the following expression:

PAL = 740 (d + h)2

L 1.3 or 70 whichever is less (14.7)



This expression has been derived from the nomogram and is and should only be used withinthe limits given in Figure 14-7.

The provisional axle load obtained is then modified by the modifying factors and thecondition factor in the following text.

Modifying Factors

Span/Rise Factor (Fsr). Flat arches are not as strong under a given loading as those of steeperprofile, and the provisional assessment must, therefore, be adjusted. A span/rise ratio of 4and less is assumed to give optimum strength and has a factor of 1. When the span/rise ratiois greater than 4, reference should be made to the graph in Figure 14-9 which gives theappropriate span/rise factor Fsr for the different ratios.

Profile Factor (Fp). There is evidence that elliptical arches are not as strong as segmental andparabolic arches of similar span/rise ratio and barrel thickness. The ideal profile has beentaken to be parabolic and for this shape the rise at the quarter points, rq = 0.75rc, where rc isthe rise at the crown.

Figure 14-9: Span/Rise Factor



The profile factor Fp for ratios of rq/rc less than or equal to 0.75 should be taken to be unity,and for ratios greater than 0.75 should be calculated from the expression:

Fp= 2 .3 rc – rq0.6 (14.8)

rc

For convenience this has been plotted in Figure 14-10.

Material Factor (Fm). The material factor is obtained from the following formula:

(14.9)Appropriate values of the barrel factor Fb and the fill factor Ff can be obtained from Tables14-10 and 14-11 respectively.

Figure 14-10: Profile Factor

hd

)h*F()d*F(F

jbm

++=



Arch Barrel Barrel Factor(Fb)

Granite whether random or coursed and all built-in-course masonryexcept limestone, all with large shaped stones

1.5

Concrete or engineering bricks and similar sized masonry (notlimestone)*

1.2

Limestone, whether random or coursed, good random masonry andbuilding bricks, all in good condition.

1.0

Masonry of any kind in poor condition (many stones flaking or badlyspalling, shearing etc). Some discretion is permitted if the dilapidation isonly moderate.

0.7

*Concrete arches will normally be of relatively recent construction and their assessmentshould be based on the design calculations if these are available.

Table 14-10: Barrel Factor

Filling Fill Factor (Fr)Concrete* 1.0Grouted materials (other than those with a clay content) 0.9Well compacted materials 0.7Weak materials evidenced by tracking of the carriageway surface 0.5*The fill factor for concrete is less than the barrel factor to allow for possible lack of bond to the arch.When assessing an arch, unless details of the fill are known or there is evidence of weakness from the conditionof the road surface, it is recommended that this factor be adopted. If the arch then requires a restriction, furtherinvestigation should be made to see if the strength shall be increased.

Table 14-11: Fill Factor

An arch which is constantly wet, or shows signs that damp often penetrates, is unlikely tohave suffered deterioration from this cause alone unless the seepage contains reactivechemicals which may have affected the materials of construction; in this case allowanceshould be made in the value taken for the barrel factor. Some local damage shall be offset byevidence that the structure was built with good materials and workmanship. Such evidencewould be:i. Durable masonry set in its correct bed;ii. Well-shaped durable stone;iii. Correct bonding of stonework or masonry with regular and narrow joints;iv. Original documents showing liberal hunching at the abutments and a good

specification.

Note should be taken of any leaching of the fill material over the arch due to the presence ofwater and this should be allowed for in the fill factor.

Joint Factor (Fj). The strength and stability of the arch barrel depend, to a large extent, on thesize and condition of the joints. Lime mortar is commonly used in bridge construction,particularly on old bridges, and, although it is softer than cement mortar, and has a lower



strength, this is compensated for by better joint-filling properties and good distributingpower under load. The joint factor Fj is obtained from the following formula:

Fj = Fw*Fd*Fmo (14.10)

Appropriate values for Fw and Fmo can be obtained from Tables 14-12 and 14-13respectively. The depth Factor Fd shall be taken as 1.0 for pointed joints in good condition.In the case of insufficiently filled joints, it is recommended that if the depth of missingmortar can be estimated with reasonable accuracy, the thickness of the arch barrel should bereduced by this amount. When this is not appropriate, the depth factor Fd shall be taken fromTable 14-14.

Width of Joint Width Factor (Fw)Joints with widths up to 6mm 1.0Joints with widths between 6mm and 12.5mm 0.9Joints with widths over 12.5mm 0.8

Table 14-12: Width Factor

Condition of Joint Mortar Factor (Fmo)Mortar in good condition 1.0Loose or friable mortar 0.9

Table 14-13: Mortar Factor

Construction of Joint Depth Factor (Fd)Unpointed joints, pointing in poor condition and joints with upto12.5mm from the edge insufficiently filled

0.9*

Joints with from 12.5mm to one tenth of the thickness of the barrelinsufficiently filled

0.8*

Joints insufficiently filled for more than one tenth the thickness ofthe barrel

At the engineer’sdiscretion

* Interpolation between these values is permitted, depending upon the extent and position of the jointdeficiency. Instead of using this depth factor, it is preferable to reduce the barrel thickness by the amount ofmissing mortar (see Joint Factor text above).

Table 14-14: Depth Factor

Condition Factor

General

The estimation of the preceding factors is based on quantitative information obtainable froma close inspection of the structure, but the factor for the condition of the bridge dependsmuch more on an objective assessment of the importance of the various cracks anddeformations which shall be present and how far they shall be counter-balanced byindications of good material and workmanship. A quantitative estimate of the arch barrel



condition factor Fc should be made by the engineer, the value selected being between 0 and1.0. A low factor should be taken for a bridge in poor condition while 1.0 shall be taken foran arch barrel in good condition with no defects. It is important that the engineer dissociatesthe "condition factor" from the "material factor" and the "joint factor" as these are dealt withseparately, as indicated in the previous text. Guidance on the choice of condition factor isgiven in the following text. Lower values than those in the suggested changes shall be takenfor an arch in a particularly poor state. When an unsound arch barrel supports a large depthof fill, a lower value of the condition factor should be taken than that based solely on theother arch deficiencies.

The condition factor of the arch, and hence its carrying capacity, can often be improved bycarrying out fairly minor repairs. These repairs are distinct from more elaboratestrengthening methods.

Cracks or Deformations

Cracks or deformations which may have occurred soon after the bridge was built are notusually as serious as those which are recent, and show clean faces, possibly with loosefragments of masonry. A further important point is whether the deterioration is progressive;where this is suspected, frequent careful observations shall be necessary before arriving at afinal assessment. Cracks may on occasion be formed in the mortar only and it is importantthat cracking and joint deficiencies should not be confused with each other.

Defects

It is also important to differentiate between those defects which affect the load carryingcapacity of the arch barrel and other defects which do not affect the load carrying capacity ofthe barrel but can affect the stability of the road surface. These are elaborated in thefollowing text.

Defects Affecting the Stability and Load Carrying Capacity of the Arch Barrel

Ranges of condition factors are given below for crack patterns resulting from specificcauses. The choice of factor is made from a critical determination of the size, shape andimportance of the various defects. The overall figure representing several defects should bebased on the relative importance of the worst type of defect present. It will not necessarily bederived by multiplying the factors for several separate defects together:i. Longitudinal cracks due to differential settlement in the abutments. These are

dangerous if large, i.e. > 3mm, because they indicate that the barrel has broken upinto independent sections. If the indications are that the barrel is breaking up into1.0m sections or less, then a factor of 0.4 or below should be used. A higher factorshould be used for crack spacings greater than 1.0m. .......................................................................................................................Range of condition factors, 0.4-0.6.

ii. Lateral cracks or permanent deformation of the arch which shall be caused by partialfailure of the arch or movement at the abutments. These faults can be accompaniedby a dip in the parapet which shall be more easily observed. .............................................................................................................Range of condition factors, 0.6-0.8.



iii. Diagonal cracks. These normally start near the sides of the arch at the springings andspread up towards the center of the barrel at the crown. They are probably due tosubsidence at the sides of the abutment. Extensive diagonal cracks indicate that thebarrel is in a dangerous state. ........................... Range of condition factors, 0.3-0.7.

iv. Cracks in the spandrel walls near the quarter points. These frequently indicateflexibility of the arch barrel over the center half of the span. .Condition factor 0.8.

Unfavorable Defects Not Affecting the Stability of the Arch Barrel

The unfavorable defects which do not affect the stability of the arch barrel but may affect thestability of the road surface are indicated below, with a description of their significance:i. Longitudinal cracks near the edge of the arch barrel are signs of movement between

the arch and spandrel or bulging of the spandrel, caused by the lateral spread of thefill exerting an outward force on the spandrels. This is a frequent source of weaknessin old arch bridges and the proximity of the carriageway to the parapet should betaken into account when assessing its importance

ii. Movement or cracking of the wingwalls is another common source of weakness inold bridges and occurs for similar reasons to i. above

iii. Where the bridge consists of multi-span arches and the strength of intermediate piersis in doubt the structure should be examined for cracks and deformation arising fromany weakness in the piers.

Condition Factor Less Than 0.4

Where the condition factor is less than 0.4, immediate consideration should be given to therepair or reconstruction of the bridge.

Application

The span/rise profile, material, joint and condition factors should be applied together withthe provisional axle loading obtained as in Provisional Assessment above in order todetermine the modified axle load which represents the allowable loading on the arch from adouble axle truck configuration with no “lift-off” from any axle.

MODIFIED AXLE LOAD = Fsr*Fp*Fm*Fj*Fc*PAL (14.11)

The unrounded value of this modified axle load should be multiplied by the appropriate axlefactors from Figure 14-11 to give the allowable axle loads for single and multiple axles.

The capacity of arches should be determined in terms of gross vehicle weights from Table14-15 in accordance with following subsection Load Capacity and Weight Restriction.

It should be noted that these allowable axle loads may not represent the strength of thebridge as a whole. This shall be affected by the strength of the spandrel walls, wingwalls,foundations, etc, as mentioned previously. Should the strength of any of these items be



assessed as being lower than the barrel strength, then the lowest value should be taken as thestrength of the bridge as a whole.Axle Lift-off

The axle factors given in Figure 14-11 cover two situations. The first, the 'no lift-off' case, isthe more usual when all the wheels of the vehicle are assumed to be in contact with the roadsurface at all times.

a) No axle Lift-Off

b) with Axle Lift-Off

Figure 14-11: Conversion of Modified Axle Loads to Single Double and Triple Axles



The 'lift-off' case relates to circumstances when an axle of a double or triple axle truck losecontact, either partially or completely, with the road surface and transfers some of its load tothe other axles in the truck. Examples of the circumstances which may bring about thisphenomenon are given below and the road condition should be inspected to determinewhether or not 'lift-off' should be taken into account. The presence of any of the followingconditions could lead to the adoption of a 'lift-off' case:

i. Vertical road alignment with a small radius of curvature, e.g., a humped back bridge.ii. Arch located at the bottom of a hill or on a straight length of road where approach

speeds are likely to be high.iii. Irregularities in road surface on the arch.

Allowable Axle Load (tonnes)Single Double Triple

Max GrossVehicle Weight(gvw)(tonnes)

WeightRestriction(Tonnes)

Type ofVehicle

11.5 10 8* 40 N/A 5 axles10.5 9.5 - 32.5 33 4 axles10.5 9 - 24.5 25 3 axles10.5 - - 17 17 2 axles5.5 - - 7.5 7.5 4WD

Table 14-15: Load Capacity and Gross Vehicle Weight Restrictions for MasonryArches

Effects of Multiple Axles and Derivation of Axle Factors

Introduction

The modified MEXE method for arch assessment makes use of a nomogram from which it ispossible to derive, for a particular arch, a provisional allowable axle load of an axle formingpart of a double axle truck. This load is then modified by various factors to allow for theshape of the arch, construction materials, dimensions of the arch barrel and any defects.However because a proportion of heavy vehicles now have triple axles, a simple method ofrelating the effect of different axle configurations to double axles is needed so that thecarrying capacity of the arch can be derived for all types of vehicle.

Theory

Examination of the stress influence lines for typical arches reveals the following:i. at positions away from the crown there is little difference in the influence line shapes

between a 2 pinned and a 3 pinned arch,ii. for a 2 pinned arch the dead load bending moment increases the live load moment at

the 1/3 point but relieves the moment at the crown.



iii. peak values for stress in the arch ring for both 2 and 3 pinned arches occur under aconcentrated load placed between about 0.1 and 0.35 of the span away from aspringing point.

These observations led to the conclusion that the critical position for comparing the effectsof different axle configurations could be taken as the 1/3 point. Examination of the influencelines also shows that the influence line for maximum stress at the 1/3 point is very similar inshape to that for the mid-point bending moment of a simply supported beam of span equal tohalf the arch span. Thus there is a simple method of comparing the effects of different axleconfigurations by comparing the bending moments due to the different loadingconfigurations on a simply supported beam whose length is equal to half the arch span.

Axle Factors

The comparisons between single and multiple axles have been done as outlined above forsingle axle and 2 and 3 axle trucks whose weights and spacing represent the extremes ofthose allowable. The basis of the method has been a comparison of the existingconfigurations with the double axle truck that was used in the derivation of the MEXEnomogram. Two sets of comparisons have been undertaken, which consider the “no lift-off”and “lift-off” cases. The “no lift-off” case assumes equal distribution of loading between theaxles of the truck. The “lift-off” case was considered because, although trucks are fitted withcompensating mechanisms to share the load between all the axles, it was felt that someallowance should be made for possible axle “lift-off” which could occur for example at thecrown of a sharply humped bridge. Recent research has indicated that for three axle trucksthe load transfer takes place between the two outer axles, the center axle weight remainingconstant. Accordingly for the three axle “lift-off” case half the weight of one of the axles hasbeen transferred to the other outer axle. For two axle trucks it has been assumed that half theweight of one axle is transferred to the other axle.

It was found that the extreme effects of the 2 axle configurations also covered the 3 axletrucks up to 22.5 tonnes. The worst case results for single axles and two axle configurationsare therefore shown in Figure 14-11 where the axle factors are plotted against the arch span.However, the vehicle fleet can include heavier 3 axle configurations of 24 tonnes with air orfluid suspension. Additional factors have therefore been included in Figure 14-11 “no lift-off” case to enable assessments for the heavier 3 axle trucks to be carried out. These mayprove to be the more onerous configuration. These factors are not given in Figure 14-11“lift-off” case because the improved compensatory performance of the air or fluidsuspension ensures that the effects of the heavier 3 axle trucks are no worse than the 22.5tonne configuration.

Curved Carriageways

Where the carriageway on an arch is horizontally curved, an allowance for the effects of anyincrease vertical loading caused by centrifugal effects should be made by dividing theallowable axle weight by the factor FA. Centrifugal effects shall be ignored when the radiusof curvature of the carriageway exceeds 600m.



Load Capacity and Weight Restrictions

To find the load capacity of an arch, the allowable axle loads determined in accordance withthe above methods should first be rounded off to the nearest 0.5 tonnes. The maximum grossweight of the vehicles which the arch can carry is then found from Table 14-15; it is themaximum weight for which both the single and, where applicable, the double axle loadcalculated for the arch are satisfied. It should be noted that when an arch has allowable axleloads which are equal to or greater than 10.5 tonnes for a single axle and 10 tonnes for adouble axle (i.e., 20 tonne truck) no weight restrictions are necessary. It should also be notedthat in the case of 5 axle vehicles with gross weights between 32.5 and 38 tonnes it is onlynecessary to consider the double axle truck configuration, since if this is satisfied any tripleaxle truck configurations up to 22.5 tonnes are also automatically satisfied.

However, heavier triaxles of up 24 tonnes with air or fluid suspensions may also be present.A check should be made to determine whether weight restrictions are needed for theseheavier triaxles. Requirements are also given in Table 14-15 to enable arches to be checkedfor 40 tonne vehicles. When weight restrictions are found necessary the restriction signs willapply to gross weights of vehicles and should be signed for one of the weight restrictionsgiven in Table 14-15.

14.5.4 SPANDREL WALLS

The adequacy of spandrel walls and dry stone walls will generally be assessed qualitativelyand be based on the results of visual inspection of the structures, including the significanceof any defects. The particular details of the two types of wall and the seriousness of thevarious defects which can occur are described in the following text.

Spandrel walls are normally formed from dressed material and suffer the normal problemsassociated with exposed masonry: weather, loss of pointing, in the joints, etc. In additiondeterioration of bridge spandrels is frequently a function of dead and live load lateral forcesgenerated through the bridge infilling or as a result of direct vehicular impact. In both casessome outward movement is caused. Lateral forces may cause the wall to rotate outward fromthe arch barrel, to slide on the arch barrel, to be displaced bodily outwards whilst taking partof the arch ring with it, or to bulge (see Figure 14-12).

Dry-stone spandrel walls are not common. Where they occur there are difficulties which aresimilar to those of retaining walls, but the effects of live loading are more significant.

Spandrel walls are more vulnerable to damage or displacement if no footway exists torestrain vehicles passing close to the side of the bridge. Without footpaths vehicular impactis more likely and the effects of the lateral loading generated by the vehicle through thebridge fill shall be more acute.

Poor bridge drainage may also be a feature leading to deterioration of the spandrel,particularly if saturation of the bridge fill occurs. It has been shown that if the fill consists ofchiseled, flat stones, the bridge may carry a larger load than if the fill is made from gravel.



14.5.5 DRY-STONE WALLS

Inspection of dry-stone walls reveals that they are normally constructed without recognizablefoundations and out of marginal quality material. Only the front face contains dressedmasonry, the remainder usually being rubble. Dry-stone walls were constructed as facingwalls to vertical or near vertical cuts in unstable or friable material or as free-standingretaining walls. In the latter cases construction and backfilling proceeded together.

Figure 14-12: Spandrel Wall Failures

The behavior of dry-stone walls is a function of their method of construction. The absence ofmortar results in stone to stone contact and since the stones used in the walls are usuallyirregular or roughly squared, point contact between stones is common. Contact pressure shallbe high especially at the base of tall stones and crushing is often evident. The open nature ofa dry-stone wall permits weathering of the face and in the open joints, reducing the area ofcontact and encouraging further crushing. In addition, percolation of ground water and



water-borne salts through the wall results in weathering and the leaching of fines fromwithin the structure.

Weathering occurs more in some areas of wall than in others, due to the very variable qualityof the masonry used. Random weathering and unsatisfactory foundations results indifferential settlements, movements and bulging, which induces acute stresses in someelements of the structure, causing cracking, whilst elsewhere stones become loose and shallbe dislodged.

14.5.6 ASSESSMENT OF DRY-STONE WALLS

Assessment of dry-stone walls consists of regular visual inspection and a comparison withadjacent structures. Qualitative judgments are difficult since conditions will vary greatlywith the quality of stone used, age, subsoil conditions, geometry, weathering factors andlocal expectations. Due attention should be given to local engineering experience.

Where past movement or the condition of the structure raises doubts concerning stability,regular monitoring should be introduced. Decisions relating to structural safety andconditions often depend upon engineering instinct, although simple visual aids such as tell-tales can be useful to determine if the structure is moving or in a temporary equilibrium.

14.5.7 SUBSTRUCTURES, FOUNDATIONS AND RETAINING WALLS

The adequacy of a sub-structure, foundation or a retaining wall is usually determined from aqualitative assessment of the general condition of the structure, including the significance ofany defects. In carrying out such an assessment, particular attention should be paid to theitems described below.

Before assessment can proceed, dimensional checks are required on the sub-structure,foundations or retaining wall for preparing sketches for analysis or for confirmation of the'as-built' drawings. These dimensional checks may require excavation or probing todetermine depth and the extent of the sub-structure and foundations. Care must be exercisedto ensure that no exploratory work impairs stability or damages underground services.

In some instances exploratory excavations, probing or boring may not be practicable prior toassessment. In these cases if an assessment is required conservative estimates may have to bemade regarding the probable dimensions of the sub-structure, foundations or retaining wallonly upon visual evidence.

In many early bridges bearings were omitted, in others only rudimentary forms of bearingwere provided. As part of the assessment the existence and efficiency of the bearings shouldbe established. Where no bearings exist or their efficiency is impaired, the ability of a bridgeto cater for thermal movements and forces should be considered.

Tilting or rotation in any direction of retaining walls and abutments shall be determinedusing normal survey techniques; if there are any indications of damage due to possiblethermal movement this shall be confirmed by using laser techniques.



Flow of water can cause leaching and scour from foundations and sub-structures; any sightof unexpected or unintended water flows should be investigated, the cause established andany resultant deterioration determined.

Underwater inspection in slow moving water shall be undertaken by divers, or using flexibledams or cofferdams. The latter may have the advantage of providing dry conditions forrepairs should they be required. In fast flowing water or in the rainy season, damming shallbe impracticable.

REFERENCES

1. AASHTO “Guide Specifications for Strength Evaluation of Existing Steel and ConcreteBridges,” 1989.

2. NCHRP 12-28(3), NCHRP Report 299, USA.3. Design Manual for Roads and Bridges, Volume 3: Highway Structures: Inspection and

Maintenance, Section 4: Assessment, London, January 1993.4. Military Engineering Experimental Establishment. "Classification (of Civil Bridges) by

the Reconnaissance and Correlation Methods." Christchurch (MEXE), May 1963.5. Hendry, A. W., and Jaeger, L.G. "The Analysis of Grid Frameworks and Related

Structures." Chatto and Windus, 1958 (rept 1969).6. Thomas F.G., and Short, A. "A Laboratory Investigation of Some Bridge-Deck

Systems." I.C.E., March 1952.7. Pippard A. J. S. "The approximate estimation of safe loads on masonry bridges." Civil

Engineer in War, Vol 1, 365. Inst. Civ. Engrs, London, 1948.8. Bridle, R. J. and Hughes, T. G. “An energy method for arch bridge analysis." Proc. Inst.

Civ. Engrs, London, Part 2, 1990.9. Heyman J. "The estimation of the strength of masonry arches." -Proc Inst Civ. Engrs,

London, Part 2, Dec 1980.10. MINIPONT User Manual, Highway Engineering Computer Branch, Department of

Transport, London, 1975.11. Page, J. "Assessment of masonry arch bridges." Proceedings of the Institution of

Highways and Transportation National Workshop, Leamington Spa, March 1990.12. Harvey, W. J. “Application of the mechanism analysis to masonry arches." The

Structural Engineer, Vol 66, No.5, March 1988.13. Chou, B. S. et al. "Finite-Element analysis of masonry arch bridges using tapered

elements." Proc. Inst. Civ. Engrs, London, Part 2, Dec 1991.

strength evaluation of existing steel; concrete and masonry arch bridges

Documents