Idea Transcript
LITERATURE REVIEW 2.1
CHAPTER 2
GENERAL
The geometrical properties of reinforced concrete members vary many a times. This variability is a consequence of inaccuracies in construction. In some cases the variability is of a more systematic type but most frequently it is random. These variations must be considered when dealing with structural safety aspects because they could present major uncertainties in a structure. The geometrical variations of reinforced concrete members can also greatly influence the cost of construction. In this chapter an extensive review of the literature connected with several aspects, such as construction errors, tolerances, deterioration of structures, structural safety and reliability aspects, is presented. 2.2
SURVEY OF CONSTRUCTION ERRORS
Codes of practice are formulated to provide guidelines on various aspects of analysis and design and to set minimum standards of safety that are consistent with economy. The earlier studies on the compliance of code specifications in construction practice revealed considerable deviation from the specified or intended practices. Rao and others (48) in their investigations conducted an extensive survey on several aspects of reinforced concrete construction. Their survey pertains mainly to the construction practices and to its comparison with the IS code specifications. The results presented pertain to two storeyed hostel block, a housing colony, and the structures of an institution. The results of their survey indicate a wide chasm between codal specification and actual practices. They suggested that some of the specifications of the codes be revised and tolerances are included for some of the parameters. The limited data presented in this article suggested that site supervision leaves much to desired at least at the most common sites. Morgan and others (38) investigated into pre pour placement of reinforcement in rectangular slabs and its compliance with relevant code requirements in Australia. They observed that the current tolerances on fixing reinforcement were not achieved on any of the sites investigated. The variations in bar placement were found to have
6
no relation to slab panel size or thickness, or to bar size and layout, for the range of slab type and layout encountered. It was mentioned that within a site, consistent workmanship can be expected although the investigation did reveal in-homogeneity of bar placement data within two sites. There were good and bad sites in each state investigated. The variations in bar placement were found to be normally distributed. There was a relation between the height of bar chairs and the mean bar position. Spacing of bar chairs for all sites was observed to be in accordance with the recommended one meter spacing. The results for the bottom cover of pre-cast panels were not significantly better than those for the other sites with in-situ panels. Robert (59) studied the distribution of bar placement errors and illustrated the influence of this error on column strength. Studies were made on bar locations in 232 columns from 12 existing buildings and it was shown that placement errors often exceed specified tolerances. In no case were bars found to be missing but placement error greater than 125mm were encountered. Strength calculations based on actual locations of reinforcement showed individual reductions of strength greater than 15 percent and for all columns a mean reduction of nearly 5 percent for high effective eccentricities.
Probability models to describe the distribution of
reinforcing placement error were derived to facilitate reliability analysis. Pfrang (46) studied the effect on column strength of varying the elements of the column cross section. He found that an increase in cover ratio, from 0.05 to 0.15 led to a decrease in strength about 10 percent for balanced load conditions where 4 percent reinforcing was concentrated in exterior layers. Roger Hauser (60) made a review of an investigation on about 800 European failures which focuses the efforts of code writing bodies to the most efficient way to maintain a given level of structural safety. It was found that the structure, itself initiates most failures due to unfavorable influences of the natural environment and incorrect introduced factors either in the planning or the construction phase. Error in the planning phase occurs mainly in conceptual work or during structural analysis. The errors in construction stage are due to insufficient knowledge or ignorance of the site personnel. It was mentioned that only very few errors are unavoidable and in majority of the cases a little additional checking helps considerable.
7
Ashraf M. EI-Shahhat et.al (3) investigated the safety of multistory buildings during construction. The safety of the structure, in these early days of its life is greatly influenced by a large no of factors including the loads, the geometry, and the material properties of the building and the method of construction. The probability of failure of the building during its relatively short period of construction is greater than that of its service life. A parametric study was performed to investigate the effect of concrete strength, spacing of forms and the construction cycle length on the construction safety. From the results, the probability of failure of multistory concrete buildings with the assumed system of construction using two levels of shores and one level of reshores ranges from about 4.3 to 13.4 percent. It was mentioned that the effect of human factors and errors during construction on the limit state probabilities should be the focus of future studies. Mirza et.al (64) studied the variability of strength and stiffness of normal weight structural concrete and suggested representative distributions for use in estimating the effect of these variations on the strength of reinforced concrete elements. This paper was based on data obtained from a number of published and unpublished sources and involves no additional laboratory tests. Mirja and MacGregor (62) have reviewed the data on dimensional variations of in-situ and precast concrete members and suggested normal distribution for various parameters for use in estimating the effect of variations on the strength of members. Their work is based on data obtained from a number of published sources Ranganathan and Joshi (53) presented the collection of field data on variations in dimensions of RCC members and statistical analysis of the same. In order to get the field data on effective depth of slabs and beams, a few slabs and beams were cast near the laboratory in the field simulated conditions and measurement were taken after chipping the concrete at randomly selected points. It was observed from the collected date that the mean deviations of (i) effective depth of slab (ii) width and effective depth of beam (iii) width and depth of column section and (iv) length of footing in plan lie within the limits of tolerance specified by the code. However, in the case of depth of beam, breadth of footing and cover of reinforcing bars in column, it was found that on average, specified tolerance was not satisfied.
8
It was also found that all variables of geometrical parameters follow normal distribution. The coefficient of variation of dimension of RC member increases with decrease in nominal size and it is equal to 4.9/nominal size of the member in mm. The reported data is based on field simulated conditions and hence its value is limited. Narasimha Rao D.L. et al (42) conducted tests on straight reinforced concrete columns with initial curvature in the main reinforcement. It was observed that the reduction of the ultimate load of a column due to dislocation of the main reinforcement is directly proportional to the amount of dislocation. The percentage reduction in the ultimate load for a maximum dislocation of 12.5 mm in a 180 mm square column in about 3.2 percent and for a 50mm dislocation it was 12 percent. In most field work the dislocation of the main reinforcement depends upon the length and size of the column, the diameter of the reinforcement bars, the type of form work and supports, the workability of concrete, and the methods of placing of concrete. In ordinary circumstances the maximum dislocation may be of the order of one to two percent of the height of the column. In such cases the percentage reduction will be less than six percent. For long columns the effect may be worse. Broms and Leroy (9) investigated the effects of arrangement of reinforcement on crack width and spacing of reinforced concrete members. The spacing and width of surface and internal cracks were investigated for long and short tensile members reinforced with one and several reinforcing bars. The average crack spacing S ave was found to increase approximately linearly with increasing distance from reinforcement as predicted by the equation Save = 2 tc where tc is an effective cover thickness. Measurements of internal and surface crack widths indicate that the average width Wave can be predicted by the equation; Wave = 2tc Es where Es is the average steel strain. The test data indicated that the average crack width depends primarily on the distance from the reinforcement(cover) and on the average steel strain, and the average crack width is independent of the steel percentage, and therefore of the size of the concrete member. Investigation of the internal crack pattern indicates that the number of cracks decreases with increasing distance from the reinforcement and that the crack width is
9
small close to the reinforcement. Measurements of the end deformations of short tension members confirm that the width of the main primary cracks, those which penetrate to the surface of the member increases with increasing distance from the reinforcement. Ranganathan and Dayaratnam (51) in their article presented the statistical analysis of typical office building floor loads. The results of the statistical analysis of the loads, and strength of concrete and steel were used in probabilistic analysis. The mean value of the floor load was observed small compared to the minimum values specified by IS code. But the coefficient of variation of load was observed high and it affects the probability of failure of the beam at different limit states. The frequency distribution of floor load in office rooms was found to be lognormal with 5 percent significance level. It was suggested that an extensive survey on floor loads in similar building may be carried out to arrive at rational values with certain confidence level for characteristic loads. Drysdale (21) in their investigation pulse velocities were measured through 1145 concrete columns in 15 structures located in Hamilton Toronto area of Canada to indicate the variability of concrete strength. The information on variability of concrete strength is intended to assist in the evaluation of the strength of existing buildings. It was concluded that poor-quality concrete can be located easily by use of ultra sonic pulse-velocity measurements where low readings simply indicate low strength. An approximate evaluation of concrete strength variation in a building can be obtained from pulse-velocity readings without performing a laboratory calibration for the concrete in question. Accurate calculation of concrete from pulse-velocity measurements must be
based
strength
on calibration curves obtained
from combined pulse-velocity and strength testing of representative specimen. The coefficient of variability of concrete strength for the columns in a building usually falls in the range from 0.10 to 0.20 but has been found to be as high as 0.30. These values agree with previous estimate of strength variability. In general it was suggested that pulse-velocity testing during or immediately after construction could be an efficient and effective method of inspection. As an
10
alternative to the standard strength tests, this procedure is far more likely to detect low strength portions of the structure and thus ensure greater structural safety and economy through immediate correction. It may be appropriate that a random sample which will provide information on quality control can be used to define the extent of testing required. John Fraczek (33) presented the details of a survey conducted by ACI Committee 348 in which 277 cases of errors in concrete structures were reported. The survey indicated that about three-quarters of the errors were actually detected by the structure with 39 cases of collapse and 172 cases of distress, cracking, spalling, leakage, settlement, deflection or rotation reported. About one-half of the errors originated in the design and the other half occurred during construction, with each phase responsible for about the same number of collapses. Of the errors due to faulty construction nearly three quarters were detected during construction and over one-half resulted in failure or distress. Most design errors were detected during occupancy and most resulted in serviceability problems. The survey only reported 11 errors detected prior to construction, with about 60 percent detected during construction and the remaining 40 percent detected during occupancy. It was recommended that a new survey be conducted to collect further information on the cause and prevention of structural failures. Tso and Zelman (74) in their paper reported on the investigation of variation of concrete strength in 403 columns in 10 buildings. A statistical analysis was done on the field data and a correlation was attempted between the measured pulse velocities and the cylinder strengths obtained from concrete samples taken when the buildings were built. The ultrasonic testing method was used. The conclusions indicated that statistical analysis of the pulse velocity data serves as a useful indication of the construction workmanship. In conjunction with some standards it is possible to assess the degree of consistency of workmanship at site condition. Constructional tolerance analysis indicated that more care should be paid to the dimensions of the form work at the top of the columns. There is a definite tendency for pulse velocities at the top of the column being less than at the bottom, which implies that the concrete at the top of the column is weaker than in the bottom.
11
2.3
CONSTRUTION TOLERANCES
Dimensions of RCC members may differ from the specified values. There may be deviations from the specified values of the cross section shape and dimensions which may be due to size and shape and quality of form work and concreting and vibrating operations.
Variations also occur in the effective depth of members. The actual
effective depth available may be different from the specified values because of improper placement of reinforcing steel bars, not providing proper cover blocks and change in values when needle vibrator are used during casting of members. Amount of variation in dimensions varies from place to place and structure to structure depending on quality of construction techniques and the training of the site personnel. Tolerances are provided in code specifications for the variations in the actual construction. Earlier studies on construction practices indicate that there is lot of deviations from codal specifications. Rao in his studies (47) observed the inconsistencies between the codes of different countries. Some of the mundane aspects of detailing such as diameter of hooks, anchorage lengths, concrete cover and corner reinforcement in slabs are discussed. It was pointed out that there is a need to bring consistency and uniformity between the codes of practice of various countries on one hand, and rationalise the specifications to make them practicable on the other. Further it was mentioned that the rational design specifications on temperature effects are still lacking despite the evidence of distress to structures when these aspects are ignored. The need for proper cover specifications and tolerances and for their implementation is emphasised. There is a need to formulate specifications for bar supports as well, in order to ensure the required concrete cover. There is further need to study the influence of several design parameters on structural performance. Morgan and others (39) in their study reviewed the provisions of the interacting Australian codes controlling concrete slab tolerances. A simplified model was presented to indicate the possible variability of top and bottom bar locations. The interacting factors contributing to the physical tolerances of RC slabs, such as manufacturing tolerances, fabrication tolerances and construction tolerances were combined to produce an estimate of possible overall variability. It was seen that Australian practice cannot achieve the present concrete cover to reinforcement and
12
effective depth requirements. Revised proposals were formulated for code changes permitting a better correlation between specification, codes and actual practices. It was observed reinforcement chairs play an important part in the pre-pour and postpour position of bars in RC elements. It was recommended that the Standard Association give consideration to the publication of a code for reinforcing bar chairs. Scanlon (61) in his article discussed a number of parameters relating to serviceability failures, particularly those involving excessive slab deflections. Problems associated with excessive slab deflections, causes of excessive deflections and building code provisions were reviewed. Interpretation of building code requirements was also discussed in considerable detail. Excessive deflections can be attributed to a combination of several contributing factors which include design, construction, materials, environmental conditions, and change in occupancy use. It was mentioned that construction errors affecting deflections under service load include, slab thickness smaller than specified,
improper
placement
of
reinforcement, particularly top bars placed too low. Improper concrete placement including inadequate vibration, lack of heat in freezing temperatures, and inadequate protection during hot weather also affects the deflection. Suggestions were made for evaluation procedures that can be used for investigating slab systems that exhibit deflection problems. Connolly and Brown (32) was made a pilot study to develop the technique for non-destructive measurement of variations in depth, width and location of reinforcing steel in existing reinforced beams and joists. The results of their study revealed that current as built structures normally exceed the design assumed tolerances. They concluded that relatively simple, inexpensive, and non-destructive methods exists for determining both over all dimension and bar placements in as built reinforced concrete structures. Also beam dimensions and bar locations can conveniently be described by well-known probability models which reflect the
inherent random nature of the
parameters used in design of concrete structures. For both top bars and bottom bars observed depth of cover tends to be normally distributed with a mean value equal to that specified by design.
13
Too much cover and too little cover appear to be equally likely, with small deviations from design cover being more likely than large ones there is a 50 percent chance that cover will be less than that specified. Based on the probability models presented, the combined effect of variability in bar placement and beam dimensions
was to reduce the ultimate moment by about 4 percent. They
recommended that advancement of the state of the art in reinforced concrete design with respect to the question of dimensional tolerances requires that this variability be taken in to account as codes specification and design practice seldom explicitly recognize the inherent random nature of various design parameters. 2.4
DETERIORATION OF CONCRETE STRUCTURES
Concrete being inherently durable the structure made of it usually requires minimal, but definite maintenance and repair during its life span. Corrosion of steel bars leading to concrete cracking and spalling is the most recurrent and damaging cause of concrete deterioration. Remedial treatment of a concrete structure damaged by steel corrosion may be effected in various ways from casual patching up to long lasting preventive repair. A repair strategy is to be formed which satisfies the protection requirements of the structure and sites the limited resources of the owner. Chung (12) in his article discussed the factors affecting the repair strategy, particular life of the repaired structure and the “trouble free period" of the repair option adopted. A systematic approach was suggested for deriving an appropriate strategy for a repair project. Hadipriono (27) in his study analysed the events in recent structural failures. A study of nearly 150 recent major collapses and distresses of structures around the world discloses the external events and deficiencies in the areas of construction and design to be the principal sources of failures. More than one-third of the surveyed structures were bridges and the remaining were low-rise, multistory, plant industrial, and long-span buildings.
The events causing these failures were categorized as
deficiencies in six areas, structural design; design detailing, construction, maintenance of the structure, material and construction of external events. Almost a third of the total number of low-rise building failures was caused by construction deficiencies, arising from false work and concreting problems. In addition, quality control during
14
concreting processes was not sufficiently enforced, concrete mixing was often conducted by means of shovels, and concrete was inadequately cured. As a result, poor quality concrete was frequently produced. Beeby (6) attempted to produce a general survey of the factors which influence corrosion of reinforcement, in concrete. The three main factors that influence corrosion were crack width, cover and mix proportion. It has been shown that crack widths have little influence on corrosion, and major parameters controlling corrosion are cover and concrete quality. It was pointed out that many design recommendations require unnecessary detailed calculations for crack control as a corrosion control measure. It has also suggested a possible approach to a more logical method of design for corrosion than the current arbitrary prescriptions. These observations were made by reference to published date from exposure tests carried out in many countries. Baweja et al (4) examined the long term performance of plain and blended cement concretes for ten individual structures. They observed that the major factor influencing concrete performance adversely was the low
initial specified strengths.
They found that chloride ion concentration profiled with in the first 50mm of the surfaces of the wharf structures and the slab on grade structures considered showed these to peak at around 20mm below the concrete surface. This could have implications on reinforcement corrosion if bars were located in these regions. Beeby (5) reviewed the evidence arising from exposure tests on reinforced concrete members relating to the influence of cracking on corrosion. This evidence gives no reason to conclude that any relationship exists between crack width and corrosion. This result was confirmed by considerations of the chemistry of corrosion of steel in concrete and the physical nature of cracks. This study was limited to the consideration of the corrosion of reinforcing bars in structures exposed to the atmosphere. Pre-stressed concrete and submerged structures are not considered. A structure, however well it is designed and constructed requires periodic maintenance. The maintenance and repair of concrete surface
may
be
necessitated due to any one of several causes, such as the effects of normal wear and tear, stresses induced by abnormal differential temperatures, inadvertent errors in
15
design, detailing and construction, exposure to aggressive environments like fire and earthquake, etc. Datta and Aggrwal (15) in processes
which
cause
their paper outlines the agencies and
the deterioration
of concrete surfaces and describes
methods of maintenance and repairs including removal of stains. Development of cracks in buildings results in loss of strength and stability, causes rain penetration, decreases sound insulation and affects aesthetics and overall efficiency. Suresh Chand (72) in his paper mentioned the task of selecting causes of cracks and suggested remedial measures to combat the situation. Methods of repair and precautions to be taken while repairing the cracks have also been described. Sirivivatnanon (66) in his paper presented a review of durability problems in reinforced concrete structures caused by lack of sufficient concrete cover and a statistical concept to analyses and to quantify in situ concrete cover in buildings. Cover data of large number of buildings in Australia and Japan were analysed. It was found that the level of confidence (LOC) for achieving minimum concrete cover for durability were poor, with less than 50 percent of the structures achieving a 90% LOC. It was suggested that an LOC of 90% could be achieved with improvements in design detailing, selection of suitable spaces and good installation practice. The correct choice of the concrete type, cover thickness and good concreting practice, could prove to be the most economical way of achieving the design service life of concrete structures. Subramanian (71) in his article described about the causes of failure of the Congress Hall, Berlin. It was observed that the collapse of the 'pregnant oyster' was mainly due to the mistakes in the planning and execution of the roof structure, which lead to the corrosion and finally to the failure of tensioning elements. The failure of this building demonstrates that the long term effects, if ignored will lead to the failure of the structure. The lessons learnt from this failure are of immense value to structural engineers. Suresh Chand (73) identified the factors responsible for the development of cracks in different type of buildings and suggested suitable preventive measures
16
for cracks from planning and designing stages to actual construction sites with a view to minimizing development of serious cracking. Blockley (8) assessed the various parameters for 23 major structural accidents and one existing structure and were analysed using a simple numerical interpretation. He observes that human errors of one form or another were the dominant reasons for the failures considered. Parameters for 23 major structural accidents showed that failures were due to a variety of causes and combination of circumstances.
However, human error, in using existing technology was the
predominant overall factor in the accidents considered. Insufficient
research and
development in formation and the resulting uncertainty surrounding design and construction decisions was also a major factor in the failures considered. 2.5
STRUCTURAL SAFETY
Leonardt (36) presented simple design rules to control cracking in concrete structures. Causes of checking and its effect in serviceability and durability are discussed. The paper was primarily applicable to large structures such as bridges. However general concepts presented are applicable to any concrete structure. Ang and Cornell (2) stressed that concept and methods of probability are the proper bases for the evaluation of structural safety, performance and the development of design criteria. Then only the effects of different sources of uncertainties can be combined and analysed systematically in a manner suitable for quantitative assessment of safety and performance.
They identify the minimum information
required for the evaluation of safety as mean value and coefficient of variation of each design variable. The authors emphasised that the lack of (statistical) data is no ground for rejecting the probabilistic basis of design. Costello and Chu (14) in their study demonstrated that when statistical data are available, probability theory can be rigorously applied to problems in the safety of reinforced concrete structures. It was also shown that if material strengths were considered to be random variables, their variation should be between a non zero lower limit and a finite upper limit. The failure probabilities derived in their article are really conditional since sources of uncertainty other than concrete and steel
17
strengths have not been considered. Future investigation into the variability of resistance, including the effects of uncertainties in overall dimensions and steel location would be useful and are contemplated. Stewart (70) in his study reported the effects of human error on a typical structural engineering design task. This was implemented by the development of a mathematical model based on Probabilistic Risk Analysis (PRA) techniques. The effects of human error are measured in terms of structural reliability. Mathematical models for two realistic quality management procedures are outlined, and the optimal procedure presented. The selection of the optimal procedure indicated that preventive measures may be more cost effective than control measures. A progressive collapse is a chain reaction of failures following damage to a relatively small portion of a structure. The resulting structural damage characteristically is out of proportion to the damage which initiated the collapse. Since progressive collapse constitutes an unacceptable hazard in many buildings, methods for its control should be incorporated in building standards. Design strategies for reducing the risk of progressive collapse was described by Ellingwood and Leyendecker (25) based on reducing the risk of initial failure and controlling the damage when localized failure occurs. 2.6
RELIABILITY
Reliability analysis forms the basis of the current engineering standards for safety evaluation. There is a universal need to balance safety, economy and serviceability in the design of a structure. Among these, safety is of paramount importance to the user. However some degree of unsafe or undesirable performance has to be accepted as absolute safety requires enormous amount of resources. The probabilistic approach to structural safety in civil engineering has been the subject of extensive studies in recent years. Methods of reliability analysis and design are well developed. Some of the significant developments in these areas are covered in this literature review briefly. The basic concept of structural reliability analysis was first outlined by Freudenthal(30). He analysed the safety factor in engineering structures in order to establish its magnitude. The safety factor could refer to design only as an entity and not to different features of it. He observed that individual safety factors for different
18
influences, such as for dead load or live load separately being inconsistent with the basic concept, could have no real meaning. Cornell (13) derived the bounds on the reliability of structural systems. His upper bound calculation represents the case when there is perfect dependence among the various load and resistance variables. Similarly the lower bound corresponds to conditions of perfect independence among model resistances and successive loads. A Monte Carlo technique was described by Warner and Kabila (75) which can be used to find the cumulative distribution functions of stochastic variables such as ultimate strength and factor of safety. Using this technique the variability in strength of an axially loaded short reinforced concrete column was investigated and the results were compared with closed form solution. A level 2 reliability study was conducted by Iyengar and Srikanth (31) to estimate the variations of strength of a reinforced concrete member in flexure and shear and to check the partial safety factors for loads recommended in IS:456-1978. The paper summarised the results obtained by Monte Carlo method. Desayi and Balaji Rao (18) have analysed simply supported rectangular doubly reinforced concrete beams, designed as per IS: 456-1978. Beams were examined for limit state of strength in flexure. Desayi and Balaji Rao (19) performed probabilistic analysis of cracking moment from twenty two simply supported reinforced concrete beams. For the assumed distributions
authors found the cracking moment to follow
a
normal
distribution. An expression for characteristic cracking moment of reinforced concrete beams for limit state of cracking was presented. Ranganathan and Deshpande (54) developed a method to verify and analyse the dominant
mechanisms in the case of reinforced concrete frames. Under the
assumption that full moment redistribution might not takes place and any critical regions might fail because of insufficient rotation capacity before a collapse mechanism is formed. A reliability model for the rotation failure prior to mechanism collapse was proposed. The safety margin equations in relation to and consistent with
19
the mechanism were generated on the basis of the partial utilisation of moment distribution at failure.
The structural reliability was reassessed by combining
rotational failure modes with other possible mechanism modes. The level of probability of a prestressed concrete section was evaluated by Ranganathan and Dayaratnam (52) using the results of the statistical analysis of strength of materials, geometric properties of section and load distributions. Monte Carlo method was used to generate random strength of a section subject to certain specifications. It was observed that normal and Type III extremal (smallest) distributions satisfy the generated data for the resisting moment of the section for under-reinforced and over-reinforced cases respectively at one percent level of significance. Probability of failure of prestressed concrete beam sections designed by Indian Standard specifications is in the order of 10-7for deterministic load and it varies from 10-10 to 10-9for probability load. Ellingwood and Galambos (24) presented probability based loading and resistance criteria that are suitable for safety checking in design. The criteria were based on a comprehensive analysis of statistical data on structural loads and resistances and an examination of levels of reliability implied by the use of current design standards and specifications. The criteria were intended to be used in specifications that are oriented towards limit state design. David Arul Rai & Ranganathan (16) in their study investigated the level of reliability in stabs designed as per the code IS.456.1978: limit state approach. The theoretical models for the resistance of slabs have been developed using yield line theory. It was concluded that the grade of steel and effective depth are the two main variables which affect the statistics of strength of RCC slabs significantly. The slabs having steel grade Fe 250 for reinforcing bars have higher reliability compared to slabs having Fe 415 bars. However this conclusion was based on the limit state of collapse in flexure. This may have to be verified considering limit state of bond strength. The partial safety factor for dead load is almost constant under different design situations and a value of 1.2 was suggested. Frangopal (29) presented an overview of the most common concepts and methods used in reliability base structural optimization in order to provide some
20
clarity and insight in to these aspects. It is interesting to note that the results obtained by sensitivity analysis can be very useful inputs for decision making in reliability modeling and control of human errors. Ellingwood et.al (22) used the data obtained from a comprehensive analysis of statistical and probabilistic information on various types of structural loads and capacities have been used to calculate reliability indices associated with existing design practice.
This provides guidance for selecting
target reliabilities for
probabilistic criteria development. Practical probability based criteria have been developed which retain the relatively simple characteristics of existing criteria and yet have a well
established documented rationale. A method has been
presented where by specification writing groups can determine resistance factors that are consistent with the load factors recommended. Moses and Stevenson (40) presented methods for incorporating reliability analysis into optimum design procedures. The approach adopted was to design for a specified probability of failure, in which the failure probability was evaluated from a sequence of numerical integrations.
The
subject
of sensitivity
of statistical
parameters was considered, with the presentation of results for the reliability based design of rigid frames, using different frequency distributions and parameters. Moses (41) highlighted the need for extending the simplified second moment code format and the extended reliability format to the structural systems problem. He also stressed the need for further research on the reliability of structural systems in connection with dynamic loadings and non linear behavior. Moses presented and discussed
some
simplified
analysis approximations including the
determination of appropriate partial safety factors for elements in systems. Ranganathan and Deshpande (56) presented a technique for reliability analysis of frames using stiffness matrix method of linear elastic and piece wise linear elasto-plastic structural analysis and the first order
second
moment reliability
method. The method involved generation of stochastically dominant mechanisms and their safety margin equations. Bounds on the system reliability were calculated.
21
2.7
MODELS FOR HUMEN ERRORS
Douna and others (20) presented some thoughts and guidelines on avoidance of gross errors, the major cause of failure of structures. Except for those cases of failure which were caused by natural phenomena, failures can often be attributed to "gross errors" in concept and planning, design, drawing, or construction practices. It was pointed out that thorough checking in the concept, planning, design and detailing stages is essential in order to avoid gross errors. Stewart and Melchers (67) developed two models to reduce the incidence of human errors in design task. The variability in design output was obtained using Monte Carlo simulation and the effect of checking observed. It was found that checking efficiencies between 0.6 and 0.9 appear to be most effective in increasing structural reliability. More realistic checking procedures were outlined and their effect on structural reliability presented. It was found that no more than three, and often only two design checks are sufficient to reduce the nominal reliability of the errorincluded design to that of an error-free design. Dayaratnam and Ranganathan (17) presented the statistical analysis of data on strengths of concrete used in different projects. They found that the strength of the concrete varies as a random
phenomenon subjected to normal or lognormal
distribution. The least-square fit of the field data of several groups of concrete indicates that the probability of failure of the concrete is of the order of 5.5%. It was stated that the strength of the concrete follows a normal distribution with at least one percent significance level if minimum control on the quality of the concrete is ensured. They indicated that a well designed concrete mix will follow the normal distribution with 5% level of significance. The reliability analysis of large and complex structural systems requires approximate techniques in order to
reduce computational
efforts to
an
acceptable level. Bucher and Bourgund (10) in their study a new adaptive interpolation scheme is suggested which enables fast and accurate representation of the system behavior by a response surface. This response surface approach utilizes elementary statistical information on the basic variables ( mean values and standard deviations ) to increase the efficiency and accuracy. Subsequently the response
22
surface was utilized in conjunction with advanced Monte Carlo simulation technique to obtain the desired reliability estimates. The proposed method was shown to be superior both in efficiency and accuracy to existing approximate methods, i.e. the first order reliability methods. The suggested adaptive interpolation procedure was shown to be a very efficient scheme with respect to both computational effort and accuracy. Ellingwood (23) reviewed the status of design and construction errors in structural safety studies. It was ascertained that a majority of structural failures and associated damage costs were due to errors in planning, design, construction maintenance rather than
stochastic
variability
and
in construction material strengths
and structural loads. A review of published failure data indicated that only about 10% of failures were traceable to stochastic variability in loads and capacities, the remaining 90% were due to other causes, including design and construction errors. A similar review of European failure data (60) indicated that 22% of failures were caused by stochastic variability but did not indicate what part of the remaining 78% was caused by errors. Lind (37) in his paper considered various models of systems with random capacity to withstand a random demand. Several empirically known aspects of the influence of human error on the probability of failure of such systems, particularly structures, were reflected in these models. Simple discrete error models of the multiplicative type showed a moderate and gradual increase in failure probability with error probability. Nowak and Robert (45) made a simple classification system for errors identified two major categories of uncertainty which cause failure is variations within accepted practice and departure from accepted practice. The second category was called as human error. Material properties dimensions, service loads and round off accuracies are recognized as uncertain within accepted practice without error. Safety factors provide protection against these random variations whose limits are called tolerances. Code provisions specifications, engineering manuals, design and detailing aids, fabrication and construction practices and checks lead towards an accepted probability of overdesign to avoid failure from variations which fall within design and construction tolerances. Ignorance, negligence and fraud are major causes of human error. Their many types include omitting, misplacing, misreading, misunderstanding
23
and miscalculating. Errors will be assumed to occur randomly but with frequencies which vary among professionals, organizations, materials, methods and structures. In practice the major difficulty is caused by the great variety of possible gross errors and events in number and magnitude. Nowak (44) in his study made an attempt to estimate the influence of the possibility of gross errors on structural safety. Four basic means of control in the occurrence rate and magnitude of the abnormal cases were discussed; these are inspection and checking, proof loading, adjustment of code safety factors and proof design. It was found that due to the variety of gross errors in number and magnitude the most efficient approach on an individual basis one error at a time. A numerical example was also provided to illustrate the influence of some possible errors on structural reliability. Neesim (43) proposed a probabilistic model for the occurrence, detection and consequences of human errors in structures. The models are developed in an overall frame work of decision theory applied to the problem of allocating control efforts that would narrow the gap between the estimated and actual rates of structural failure. The probability models presented are intended for application to decision regarding the optimal efficiency of control measure by providing a link between the efficiency of a given error control measure and reliability of the structure. Reliability based analysis permits a more consistent approach to structural safety by including the statistical variability of loads and strengths in the safety factor evaluation (34). Evaluation of reliability allows one to formulate a rational design and optimization procedure. It is furthermore necessary to include types of failures other than collapse in the reliability analysis to obtain an overall optimum design Kapse and Bela Rani (35) briefly summarize in their paper the various investigations that have been directed towards understanding the corrosion and protection of steel reinforcement in concrete. Sibly and Walker (65) in their paper presents reviews of the histories of four large metal bridges which failed either during construction or shortly after being brought into service. From this material the Authors conclude that the accidents had
24
certain causes in common and that their histories hold lessons for present day engineering practice. Stewart (69) conducted a survey to estimate the percentage of construction sites that exhibit poor, fair, or good levels of performance for each construction task. An "overall probabilistic model" of concrete compressive strength was developed from these survey data. The overall probabilistic model represents the variation expected between buildings. It was found that poor curing is most detrimental to concrete compressive strength, and that the proposed probabilistic models are best represented by the lognormal distribution. Udoeyo and Ugbem (28) undertaken an investigation on the variations in dimensions of reinforced concrete member resulting from construction activity in Nigeria. Poor inspection enforcement during construction, among other factors, was identified as being responsible for the geometrical imperfections of the studied members. Based on this study, normal distributions are recommended to represent the probability models of all the imperfections. This was established by the goodness-offit test conducted on the data obtained. The recommended mean deviation from nominal dimensions and the corresponding standard deviation for slabs, beams and column are given. Human errors, particularly in design have been found to be the dominate cause of structural failure. Stewart and Melchers (68) developed an “economic decision” model for evaluating the optimal level of design checking using expected utility at the criterion for decision making. The model was developed for a simple structural member using previously reported data on the process of member design and a design checking. It was found that the use of thorough self checking and overview checking only was the optimal strategy, unless the consequences of failure are expected to be catastrophic, in which case one independent design check is also necessary. In principle, the model should be valid for any structural engineering decision making application. A large proportion of structural failures are due to human error in the design stage of a structural engineering project and many of these failures could have been averted if there had been adequate design checking.
25
Stewart and Melcher (67)
reported survey data and mathematical models for three design-checking processes. The processes appropriate to design checking are self checking, independent detailed design checking, and overview checking. It was shown that relatively simple models may be developed for component of these design checking processes. The variability of the short time ultimate strength of rectangular cast-in-place slender tied reinforced column bent in single curvature was studied by Mirza and MacGregor (63). The variation in material strengths and geometric imperfections on the ultimate strength were determined. The results indicated that the longitudinal steel ratio, the slenderness ratio, and the end eccentricity ratio had significant influence on the probability distribution properties of the slender column strength. The necessity of treating the variation of live loads probabilistically is well recognized by many researchers in the safety analysis of structures. Although there are accurate techniques available to assess structural behavior under given loads, yet the loads themselves remain an estimate to be computed based upon field measurements, professional logic and experience. With this need Chalk and Corotis (11) developed a probabilistic format for the determination of building floor live loads upon examination of live load data and the behavior of live load process. Ellingwood (26) developed probability distributions and statistical parameters for wind and snow loads using the available data. He found that in majority of reliability studies the Cumulative Distribution Function (CDF) of load was not described and attempts were only made to match the CDF of the load in its centre range. On the other hand Ellingwood's procedure fits the CDF of the load in the region of safety checking point. Ranganathan and Chikkodi (55) derived the partial safety factors, using advanced level 2 approach, for reinforced concrete design as given in IS: 456-1978. The paper explained the methodology, as well as the assumptions made in the derivation of partial safety factors. Curves for the selection of partial safety factors corresponding to a given reliability were presented. Ranganathan (57) analysed wind speed and wind load statistics for probabilistic design based on data obtained from different geographical stations in
26
India. He assumed that the established statistics of wind speed and wind load can form a basis for the calibration of Indian Standard code on reliability theory. Benjamin (7) described some of the advantages of rational probabilistic analysis and design concepts compared to deterministic procedures. He observed that deterministic procedures are inferior to probabilistic concepts in informational content, modeling of reality, refinement of analysis and design and the resulting structures. Raj and Ranganathan (50) investigated the reliability level in slabs designed as per IS: 456-1978 using limit state approach. The reliability index and partial safety factors for loads and resistance were determined using level 2 approach. Curves were drawn for optimal safety factor selection for different design situations.
2.8
SUMMARY
A review of statistical analysis of structural failures reveals that many a structural failure and associated damage costs are due to errors in planning, design, construction and maintenance. Probabilistic concepts are used extensively in current design methods and in reliability analysis. However these methods do not take into consideration field errors in design and construction. The reliability of a structure can be substantially enhanced by controlling field errors. 2.9
CONCLUDING REMARKS
Errors occur in all phases of building process, planning, design, construction and maintenance. A review of statistical survey of structural failures reveals that many a structural failure is due to errors rather than variability in construction material strengths and structural loads. These findings have raised considerable interest in studying the role of field errors in structural performances. The major deviations in the specifications and practices adopted in the construction need further study. In this regard an attempt has been made to collect data regarding the cover to reinforcement in slabs, beams and columns of different types of buildings where in different levels of quality executions are exercised. The data obtained is statistically arranged for further generations to use it in a scientific way.
27