Guide to Compressive Membrane Action

7 ; Prepared for the - - - Concrete Brldge Development Group

. . : . ' . . ,

A Guide to Compressive Membrane Action in Concrete Bridge

Notation

Summary

1.0 Introduction

2.0 Bridge deck slab design

2.1 T~ltroduction

2 2 Global and local behclr lour

3 3 British design codes

3 4 Other bridge design codes

2.5 Summan. of bridge design

3.0 Review sf literature

3.1 Introduction to compressi\-e membrane action

3 3 Early research

3 3 Research b!- Park

3 4 Research at Queen's Unir crsity Belfast

3 5 Research at Un~~ers~ t \ . . College. London

3 6 Research at Cambridge Unn ersit\

3 7 Other research 111 the UK

3 S Research 111 Canada

3 9 Other research centres

3 10 Re\.ie~v of d!~namic/fatigue load tests

3 1 1 Summan. of methods

4.0 Sarnrmary of methods for predkctirmg the strength of lateraIly restrained bridge deck slabs

4 1 Introduction

4 2 Comparison to the existing code (BS5100)

4 3 Queen's Unixws~t! of Belfast approach

4 4 Park's method

5.0 ConcIudlng remarks

Tables Appendix Bibliography

cross sectional area equivalent area of support beam area steel reinforcement compressive arching force con~pressive bending force compressive force in concrete compressive force in reinforcement concrete elastic modulus second moment of area of support beam about the vertical axis axial stiffness eqivalent stiffiless of support beam stiffness of diaphragm and slab combined stiffness of restraint stiffness of slab within effective width half the span of the arch length half the span of the rigidly restrained arch arching monlent of resistance

M.,(,,,,,, maximum possible arching moment of resistance arching moment of resistance of rigidly restrained slab strip flexural moment of resistance at principal section balanced moment of resistance moment ratio (non-dimensional) applied load predicted ultimate arching capacity predicted ultimate flexural capacity predicted ultimate flexxral capacity from BS5400 predicted ultimate capacity under Kirkpatrick et al's method predicted ultimate capacity under proposed method predicted ultimate capacity under Park's method measured ultimate load of test model predicted ultimate punching shear capacity from BS5400 flexural punching strength shear punching strength McDowell's non-dimensional parameter (elastic deformation) tensile force in reinforcement

width of section effective width of loaded slab critical perimeter width of square patch load n-idth of patch load parallel to slab span width of patch load perpendicular to slab span effective depth of slab half the arching depth concrete cylinder compressive strength concrete compressive strength concrete indirect tensile strength reinforcement yield strength depth of slab arch height arch height Kirkpatrick et al's arching moment coefficient shape factor h.IcDowell's maximum compressive stress McDoweIl's non-dimensional parameter (deflection) deflection under the load point depth of concrete compression zone proportion of d l in contact with the support proportional depth of stress block (=0.9 in BS) deflection under the load point strain concrete compressive plastic strain value concrete maximum compressive strain width of circular patch load reinforcement ratio at principal section effective reinforcement ratio at principal section effective archiig reinforcement ratio at principal section stress

Summary Slabs in beam-and-slab bridge decks are nornlally designed for global bending effects and local bending and shear stresses These are resisted by conventional reinforcement in the top and the bottom of the slab. However it is widely accepted that, in addition to the strength provided by the reinforcement, bridge deck slabs have an inherent strength due to the in-plane arching forces set up as a result of restraint provided by the slab boundary conditions This has been attributed to compressive membrane action (CMA) and by adopting arching theory it is possible to produce bridge deck slabs which have lower quantities of reinforcement and are, therefore, both more economical and more durable.

In the past 30 years it has become increasingly evident that corrosion of reinforcement due to the effects of de-icing salts has been one of the major factors in the deterioration of reinforced concrete bridge decks. Detailing to reduce the risk of corrosion is simpler if the percentage of conventional reinforcement is low. It has been recognised for some time that restrained slabs and beams exhibit strengths far in excess of those predicted by bending theory (Turner, 1909). However, the phenomenon has remained largely esoteric for the practising engineer.

If the edges of the slab are restrained against lateral movement by a stiff boundary, an internal arching mechanism or Compressive Membrane Action is induced as the slab deflects. This enhances the flexural load capacity of the slab. The arching phenomenon occurs in concrete due to the significant difference betw-een its tensile and compressive strengths. The weak strength in tension causes cracking due to the application of load. This shifts the neutral axis towards the compression face. If the edges of the slab are restrained by a stiff boundary, internal arching action is induced (Fig 1).

The enhancement in slab strength, due to arching or Compressive Membrane Action (CMA), has been incorporated into some design standards, including the Department of Regional Development (NI) 'Design Specification for Bridge Decks' (1990) and more recently the draft design guidance, BDS 110 1, 'Use of Con~pressive Membrane Action in Bridge Deck Slabs'. This highlights the practical application of a design theory which allows for compressive membrane action in such decks

Fig. 1 : Compressive membrme action in laterally restrained reinforced concrete siab

It has been well documented that the degree of lateral restraint has a beneficial effect on the strength of restrained slabs and bridge decks have inherent restraint due to the presence of diaphragms, supportin,a beams and the surrounding area of deck slab Similarly, concrete strength has a significant effect on the arching capacity. Therefore, by utilising the advantages of high strength concrete and lateral restraint it should be possible to produce deck slabs with very low percentages of reinforcement

This report presents a review of the literature in regard to CMA in bridge deck slabs. The design procedures developed at Queen's University of Belfast and the University of Canterbury in New Zealand are considered in detail together with a typical example of the Queen's University procedure for predicting the strength of laterally restrained slabs.

2.0 Bridge deck slab design

2.1 Introduction

New bridges are usually designed to a Code of Practice, in the UK this is BS5400, Part 4 (1990) and the associated Highways Agency Standards (BD's). Similar standards or codes exist for the assessment of existing structures. These codes have been developed either from an accepted rational theory or from empirical formulae based upon experimental evidence and engineering experience. Therefore, any new design or re-discovered design concept, such as compressive membrane action, is unlikely to be accepted in modem design unless it is included in the relevant design codes Compressive membrane action has only recently been included in the draft BD81101 and, to date, has remained largely unused in design This guide aims to address one obstacle to the use of BD8 1/01 by setting out in detail the method by which the capacity of a laterally restrained slab can be calculated.

2.2 Global and local behaviour

The global behaviour of a bridge structure is determined by the overall distribution of forces and deflection both longitudinally and transversely. This analysis is normally carried out for a complex envelope of loads I-epresenting the many different load combinations which are achievable. The local behaviour is the effect on a particular element of the structure caused by individual loads, for example, a wheel load on a section of the deck slab In the design, and the assessment, of bridge structures it is difficult to assess the combined effects of both the local and the global load Therefore, in most cases, the two effects are treated independently. In the UK, bridge designers combine the worst coexistent local and global load effects and the detailed analysis subsequently examines the stresses at particular elements in the structure In the design of the deck slab of a beam-and-slab type bridge it is generally the local effects which dominate Therefore, the focus of this guide is on the design of the deck slab in relation to the local effects

2.3 British design codes

Currently the British Standard for reinforced concrete bridge design (BS5400 Parts 2 and -I), in conjunction with the Departmental Standards BD15192, BD24192, BD37101 and BD44195 reconmends the use of Westergaard's (1930) or Pucher's (1964) charts to assess the local effects of wheel load This generally gives a level of transverse reinforcement of between 1 2% and 1.7% in the deck slab However, these charts have been developed from plate theory assuming a linear elastic material and are not representative of the behaviour of a restrained reinforced concrete slab. In other words, the effect of membrane action has been neglected.

A detailed program of field tests in Northern Ireland showed the deck slabs of RI-beam type bridges with reinforcement ratios of less than one third of those calculated using the design charts performed satisfactorily. In addition several laboratory models tested with reinforcement ratios as low as 0 25% behaved adequately. Subsequently the Northern Ireland Standard (DRD, 1990) was amended to reduce the amount of reinforcement The code suggests the use of 0 6%, top and bottom, transverse reinforcement in the deck slab of M-beam type bridges nith a main beam spacing of 2111 or less This includes a fairly high safety margin based upon the results of field tests but halves the amount of reinforcement compared to that predicted by the use of Pucher's or Westergaard's methods.

There are, however, a number of limitations in the use of this standard. The span to depth ratio is restricted to less than 15 and the tests (Kirkpatrick, 1984) were based on a 160mm-deck slab The code recognises the lack of lateral restraint in edge locations of the deck, compared to the interior sections Therefore, the edge cantilevers are designed by the conventional methods and this generally requires greater percentages of reinforcement.

Following the work by Kirkpatrick and Rankin the Highways Agency has now produced a draft design guidance BD8 1/01, 'Use of Compressive Membrane Action in Bridge Deck Slabs' This draft is currently being finalised but outlines the Queen's University of Belfast method developed by Rankin and Kirkpatrick However, the same limitations apply as to the NI design code and for slabs outside this criteria it is not clear how to assess the d e ~ r e e of external lateral restraint

2.4 Other bridge design codes

There are hndamental differences in the methods adopted for the analysis of bridges throughout the world and t h s is reflected in the relevant design codes For example, bridge engineers in the LK combine the worst effects of the local and global loads In USA the deck slab is generally designed for the local effects; the section is then deemed adequate for the effects of global loading This is valid for the majority of bridge structures used; namely, steel-concrete composite beam-and-slab bridges ~vith internal diaphragms

A small number of countries have adapted their codes to recognise the presence of compressive membrane action In addition to Northern Ireland, which has already been mentioned (DOE, 1990), the Canadian Code (OHBDC, 1992) has reduced the reinforcement requirements These incorporate n~ostly empirical design rules based upon the results of field and laboratory tests The Canadian code (OHBDC, 1992) recommends 0.3% isotropic reinforcement in a deck slab with a minimum thickness of 225mm. The span to depth ratio is limited to less than 15 which corresponds to a maximum slab span of 3.7m. The code requires additional reinforcement in certain circumstances, such as at the ends of highly skewed decks where the amount of reinforcement is doubled; though recent research (Bakht and Aganval, 1995) has suggested that this is too onerous Following a series of fatigue tests on similar skewed deck slabs (Bakht et al, 1996a), an addendum to the OHBDC code has been made. This removes the restriction for additional reinforcement provided the explicit in-plane restraint has been provided, most commonly by steel channel diaphragms placed with the web in the horizontal plane.

2.5 Summary of bridge design

There are substantial differences in the methods of design and the forms of construction adopted for bridge structures throughout the world. The most common form of bridge construction in the latter half of the twentieth century has been the beam-and-slab type

structure In North America this tends to be a steel/composite slab form but in the UK, pre-cast concrete beams are also common Thus, theory based on a reinforced concrete deck slab is relevant to both forms of bridge structure

As already stated, the global loading has an effect on the transverse moments but it is the local loading which has the dominant effect. Traffic loading creates an infinite variety of load combinations but for the deck slab the niorst position is a concentrated load at the midspan of the slab With the exception of a few codes (OHBDC, 1992 and DRD, NI 1990) the effects of compressive membrane action have been ignored although the slabs in a typical beam-and-slab bridge deck have inherent restraint and represent a structure ideal for the development of compressive membrane action

3.0 Review of literature

3.1 Introduction to compressive membrane actfoil

If the edges of a loaded slab are restrained against lateral movement by a stiff boundary, an internal arching reaction or compressive membrane force is induced as the slab deflects (Fig. I , p. 1 ) The behaviour at low loading is elastic, region A to B in Fig.2, but reaches an elastic- plastic phase, B to C, prior to the peak load at C. This peak load corresponds to the maximum arching effect and, in under reinforced slabs, the maxinium bending strength. At increased deflection, the subsequent load capacity reduces.

Midspan deflection +

Fig. 2 : Typicid load vs. deflection for restrained reinforced concrete s h b

The following sumiiiarises the wealth of literature covering compressive membrane action with specific attention to bridge deck slabs It has been shown that the arching effect is relatively greater in slabs with lower reinforcement percentase, low span to depth ratio and a high degree of lateral restraint That is, in comparison to the flexvral or yield line predicted ultimate strengths which do not consider membrane effects.

3.2 Early research

The phenomenon of 'arching' has been recognised by engineers for many decades Turner i n 1909 was one of the first to acknowledge arching effects when he wrote 'such a slab will at first act somewhat like a flat dome and slab combined' In 1921 Westergaard and Slater described the effects of arching but in the ensuing years most research appears to have followed an alternative path The first serious endeavour to rationalise ChfA in analysis was in the So\.iet Union when Gvodzev (1936) published a paper referring to the Russian code of practice for reinforced concrete, which took into account arching action. However, it was probably due to the pioneering work of Johansen, on yield lines, that most other research in this field followed another route and, combined with the effect of the Second World War, the arching phenomenon did not regain interest until the 1950's.

It was brought to prominence in 1956 when Ockleston published the full-scale loading test results from the Old Dental Hospital in Johannesburg. The measured failure loads were considerably higher than those predicted by yield line theory, which had become globally accepted at the time. Some years later in South Africa, Liebenberg (1966) carried out field tests on an eight-storey reinforced concrete building in Cape Town which clearly illustrated the nature of CMA. Around the same time that Ockleston was carrying out his work, arch action i n masonry panels subjected to transverse loading was observed by hllcDowell et a1 (1956) They proposed a theory for arching action which represented a radical deviation from current thinking at that time.

Brotchie (1963) used classical elastic theory to provide a solution for the capacity of restrained slabs but did not consider an elastic lateral restraint. Also in 1963, Christiansen developed a theory for one-way spanning slabs restrained by a flexible boundary. Nearly two decades later Christiansen (1983) published two papers setting out a simplified approach to assess the strength of laterally restrained slabs based upon the following:

Brn = Ptest - Pj WWI \%-here P,,, = load due to con~pressive membrane action

P,,,, = maximum total load on the slab P, = Johansen's loads (i e flexural capacity using yield line analysis)

Although it was appreciated that the flexural and arching effects were not separate mechanisms in reality, the consideration as two independent effects was put fonvard as a rational approach for predicting the peak load. Taylor and Hayes (1965) carried out tests on 22 unreinforced and reinforced square slabs in pairs. They concluded that the enhancement in strength was greatest in the pairs where the simply supported model had been close to flexural failure prior to punching, that is, in the slabs with a lower percentage of reinforcement Roberts (1969) conveyed his theory for slabs with varying restraint conditions although the tests carried out included of a relatively stiff surround compared to slabs in practice. Compressive nlembrane action received significant attention in 1971. The American Concrete Institute held a seminar, which was aimed at bringing together researchers in the field of concrete slab systems The special publication (SP30-14, 1971) contains several papers devoted to compressive membrane action.

-4 gzm& 10 can~pressi\v membrmre crcirorl in bridge deck slabs 6

3.3 Research by Park

Park has been one of the major contributors to research into compressive membrane action and actually devotes a whole chapter to the subject in his book (Park and Gamble, 1980) Park (1961a) presented a theory where the ultimate moment of a rigid-plastic strip was determined, based upon a yield line pattern and using horizontal equilibrium combined with geometric compatibility. Park concluded that, due to the sensitivity to the concrete strength, the strength of restrained slabs is highly dependent upon the stress diagram employed in the calculations He used Hognestad's relationship, which assumed an elasto-plastic material property.

Later, he presented a refined theory which included an adjustment for the lateral restraint and axial strain, caused by shrinkage and creep in the concrete (Park, 1961b). The following year, Park (1965) presented the results of tests on twenty small-scale mortar models where the span to depth ratio varied between 18 and 30. Park refined his theory and summarised the many years of work in his book (Park and Gamble, 1980) and his method is discussed later.

3.4 Research at Queen's University Belfast

In the late 1970's the effects of compressive membrane action were being investigated at Queen's University, Belfast and have continued until the present day. Masterton and Long (1 974) first suggested that the punching strengh of slab-column structures would be enhanced by the development of CLMA. Later, Rankin (1982) developed a rational approach for the strength of laterally restrained reinforced concrete slabs. Rankin allowed for a less than rigid restraint by using the analogy of a three-hinged arch (Fig.3). The analysis was exxended to predict the strength of two-way spanning slabs, under a concentrated !oad, by u i n g a two-phase approach, similar in concept to that proposed by Long (1975). It separately predicted the enhanced flexural and shear punching strengths of the slab and the ultimate strensh was the lesser of the two values.

a) elastically restrained arch

b) equivalent rigidly restrained arch

Fig. 3 : Analogy of three-lringed arch (Rankin, 1982)

In 1987 Rankin published his refined theory including the effects of compressi~.e membrane action Rankin attempted to pro~ide a relatilrely simple method for the prediction of flexural and shear punching strengths of interior slab colurnn specimens and he showed that the theorjc provided more realistic values for the actual strength compared to the design codes While there is general agreement for the bending strength of slabs there are major discrepancies betneen the design codes for the prediction of shear stren,nth The British Standard equations for shear have been developed from nork by Regan whereas the American codes ha1.e progressed from the theories of Moe

ParaIlel to the work by Rankin at Queen's University, Kirkpatrick (1982) was investigating arching in the deck slabs of M-beam bridge deck slabs. This included both field and laboratory tests and is summarised in several papers. The first paper (Kirkpatrick et al, 1982) described tests carried out on four bridges around Northern Ireland and a subsequent paper (Kirkpatrick et al, 1984a) presents the punching strength test results on a third scale model of Clinghan's bridge The analysis of punching was developed by modi@ing Rankin's model and the arching capacity was given by the equation.

M,, = k. f c.h2 where k = u . M , ( h41 = 4 for rigid plastic material [Eqn.2] 4 < I for elastic-plastic material)

It was postulated that the arching effect could be equated to an 'equivalent' reillforcement percentage which had a similar effect on the depth of the neutral axis. By the substitution of the equivalent reinforcement index into the equation for the punching shear strength the enhanced punching strength was established The theory showed good agreement for thick slabs (span to depth ratio less than 15) with near rigid restraint and showed that the then current design codes were highly conse~at ive. A second paper by Kirkpatrick et al (1986) presented the results of serviceability tests on the actual bridge, Clinghan's bridge In this paper they reiterated the conservative nature of the design codes. Westergaard's charts, used to establish the effect of local wheel loading, had required 1 776 transverse reinforcement However, the actual range was detailed with between 0 25 and 1.7% transverse reinforcement and, under an abnormal wheel load of 1 12 5kN, all the regions of the deck slab remained uncracked. They concluded that co~npressive membrane action controlled the onset of cracking and that the BS5400 semi- empirical equation for the prediction of crack widths was not applicable to restrained slabs

In the same pear another researcher at Queen's University, Niblock (1986), proposed an analjtical method for predicting the strength of restrained slabs under uniformly distributed loading At about the same time Skates (1987) was investi,oating the feasibility of utilising arching action in cellular structures. Ruddle (1989) considered the effect of compressive membrane action in laterally restrained rib slab systems.

In 1988 Long et a1 presented an overview of the tests on h4-beam bridge decks. It was concluded that the percentage of reinforcement in the deck slab could be reduced to 0.6% with a beam spacing of between 1 5 and 2113 This represented a 35% saving in the cost of a typical bridge deck. It was shortly after this that the Department of the Environment (Northern Ireland) modified the bridge design code to allow for compressive membrane action if certain conditions of restraint were present The following year Long and Rankin (1939) published an overvjew of research where the vast majority of the tests show strengths far in excess of those predicted by the current theory. This was mainly attributed to the presence of arching action. A subsequent paper in 1995 (Long et al, 1995) highlighted the benefits of including compressive membrane action in bridge assessment In 1997 Rankin and Long presented, in detail, Rankin's theory for the predicting capacity of laterally restrained slab strips.

Some of the most recent research at Queen's University of Belfast into compressive membrane action investigated its effect in continuous steellconcrete composite floor slabs (Peel-Cross et al. 2001) More recently Taylor et a1 (2001a) presented the effects of compressive membrane action in high strength concrete bridge deck slabs It is known that the compressive strength of concrete has a significant effect on the strength of laterally restrained slabs. This research extended the existing knowledge of compressive membrane action for concrete ~vith compressive drenghs up to 100~1mm' and by utilising the advantages of high performance concrete it was possible to produce decks with very low percentages of reinforcement. Fifteen one-way slabs typical of a section of bridge deck were tested. The variables included concrete strength, degree of edge restraint and the percentage, position and type of reinforcement.

The extent of arching action is dependent upon the degree of lateral restraint and this has proved difficult t o quantify Taylor (2000) provided a method for assessing the degree of lateral restraint by using a restraint model and this is described more hlly in section 4.4. Taylor et a1 (2001b), developed a method for predicting the ultimate load carrying capacity of bridge deck type slabs with a range of boundary conditions The proposed method was found to more accurately predict the strength of these slabs compared to current methods. The research also investigated novel ways in which the slab could be more effectively and efficiently reinforced This included the use of polypropylene fibres within the concrete which reduce thermal and shrinkage cracking to further enhance the long term durability.

3.5 Research at University College, London

In the 1980's and 1990's research into compressive membrane action in the LK was also being carried out under Morley in Cambridge University and Keinp and Eyre in University College, London. Eyre and Kemp (1984) postulated that the load enhancement versus deflection relationship was a reflection of the yield curve for rigidly restrained slabs. In 1990 Eyre highlighted the difference between flow and deformation rules and concluded that for a rigid- plastic system the two rules give identical solutions for the membrane force at maximum deflection Eyre's theory predicts a safe working load for a rigidly restrained slab from the calculated total load versus deformation response.

Eyre and Kemp (1994) provided evidence that the axial stiffness of the slab was dependent upon the stress state in the slab and much smaller than the stiffness given by the full depth of the slab Most rigid plastic theories (e g , Christiansen, Roberts, and Braestrup) assume that the stiffness is given by the following equation.

K= E.A [EW.31 L/2

Other researchers reduced the value to account for the cracked section properties. Eyre suggested a value of stiffness incorporating only the area of concrete, which was hl ly stressed, similar to Rankin (1982).

3.6 Research at Cambridge University

Recent work was highlighted in a paper by Kuang and Morley (1992) Tests were carried out on twelve restrained slab specimens at 115 scale. Contrary to the effect of the reinforcement found in the tests at Queen's (Kirkpatrick, 1982), they found a 51% increase in the non-dimensional strength of the 40mm thick slab when the reinforcement was increased fiom 0 3% to 1.0%. However, this particular slab had a high slenderness value and was, perhaps, not typical of many

d gzu~le to con~pre.s.si~v n~emhrzrr2e acfiorr it? 1T1ricfge deck sInhs -- 9

structures in practice, particularly bridge decks Kuang and Morley \yere in ageement lvitli most other researchers in concluding that the degree of edge restraint was significant to the ultimate strength of the restrained slabs They also recognised that the presence of arching played an important role in controlling cracking. The ultimate strenghs were much greater than the punching strengths predicted by both the British Standard (BSSI 10) and the American code (ACE 18-89) which highlights the conservative nature of the design codes A paper the following year (Kuang and Morley, 1993) described a plastic theory using hlohr's failure criterion for the punching shear. The most recent no rk at Cambridge in this field was published the following year (Morley et al, 1995). This described the 'Galerkin' approach to computing the capacity of restrained slabs. A stiffness ratio was adapted to model the edge restraint and the procedure considered both a rotational and lateral restraint

3.7 Other research in the UK

One of the first attempts to incorporate finite element analysis into arching theory was by Cope and Rao (1977) and a subsequent paper (Cope et al, 1979) used a non-linear finite element analysis (NLFEA) for determining the strength of bridge deck type slabs. Jackson, 1989, presented an elastic method for predicting the strength of a restrained slab strip but he only considered an unreinforced strip. He went on to outline a relatively sin~ple non-linear finite element analysis which accounted for membrane action in bridge deck slabs.

Jackson validated the analysis by testing two half scale bridge models under full HI3 loading He concluded that diaphragms were not required to enable the development of compressive membrane action but restraint was inherent in the surrounding under-stressed material This followed similar conclusions by Rankin (1982). Jackson's laboratory tests were some of only a few which considered the effects of compressive membrane action on the global analysis Jackson determined that the failure mechanism was 'influenced by the global behaviour'. In 1990 Jackson and Cope published several papers outlining the advantages of compressive membrane action in the design and assessment of bridges particularly where costly strengthening programmes would be the alternative

Research at Bristol University into compressive membrane action has been described by Lahlou and Waldron (1992) They tested three slab strips v,ith varying end wall details and the results were compared to a NLFEA package called ANSYS, vvhich consisted of an 8-node solid element with two degrees of freedom at each node and showed good agreement The most recently reported research in the UK into compressive membrane action has been at Aberdeen University. Famiyesin and Hossain (1998) made use of a FEA package to develop a series of design charts. The FEA package had been verified using the results of several test models. The charts showed good agreement with 36 test results reported in literature. However, the charts are only valid for rigidly restrained slabs and therefore have little bearing on the strength of many bridge deck slabs in practice

3.8 Research in Canada

I-Iewitt and Batchelor (1975) presented a rational theory for membrane action and the following year Batchelor and Tissington (1976) advanced the research They implemented tests on bridge models and suggested a theory, based upon Christiansen's concept of a combined flexural and arching moment Batchelor et a1 (1978) set out a detailed test progranme to assess the endurance limit of slabs with a various amounts and arrangements of reinforcement Five models of a steeVconcrete composite type bridge, at '18 scale, were tested The tests at Queen's University, Ontario, led to hrther tests on actual bridge structures in a comprehensive study

A grtidt? to con7pressi~v ntembrcrne actro?? itr bridge deck slcrhs 10

sponsored by the Ontario Ministry of Transport. Subsequently the design code (OHBDC, 1979) was changed to allow a reduction in reinforcement to 0.3% in the deck slabs provided certain boundary conditions existed

In the 1980's and 1990's research into the behaviour of bridge decks continued to be prevalent in Canada Bakht, Mufti and Jaeger have published many papers on this subject In 1992, Bakht and Jaeger summarked the results of tests on short span simply supported 'slab on girder' bridges. The transverse distribution of loads appeared to improve at higher loads. The FEA packages adopted were capable of modelling arching by incorporating sufficient degrees of freedom to allow for the in-plane restraint. The following year, Mufti et a1 (1993) carried out tests on M-scale bridge models containing no conventional reinforcement The third model included external straps welded to the underside of the top flanges. This provided sufficient lateral restraint to ensure a punching failure at a load far in excess of the required ultimate bridge loading. However, the total area OF the steel straps was equivalent to a 1 4% area of conventional reinforcement, which is over three times the current recommendations in the Canadian bridge code (OHBDC, 1992). Another possible problem with external straps is the introduction of increased maintenance in the life of such a deck. A second paper (Thorburn and Mufti, 1995) details the second series of test using similar models to the above A range of values for the external restraint was established and a preliminary method adopted for optimising the value of the required restraint.

In 1995 Selvadurai and B a h t provided information on tests simulating a rolling wheel load on a FRC deck. The tests were carried out on full-scale laboratory models and it was concluded that the decks could adequately withstand four million passes at 98kN loading which was greater than the equivalent working bridge load The same year Bakht and Aganval (1995) presented the results of test on a series of third scale model skew bridges. These were aimed at testing the ability of arching action in the end regions of slabs in highly skewed bridges They concluded that it was not the geometry of the structure but the degree of lateral restraint which governed the strengh of this region of the deck slab

Bakht et a1 (1996) sun~rnarised the recent work on steel-free bridse decks. They outlined the current requirements in the OHBDC for a 0.3% isotropic mesh and emphasised that the main cause for the deterioration of existing bridge decks was the corrosion of the reinforcement. They emphasised that decks devoid of steel reinforcement have hisher durability and m-here structural reinforcement is required, such as that catering for the hogging moment in the cantilevers, plastic reinforcement was preferable. A rudimentary cost analysis on this type of deck predicted an increase of only 8% in the cost of the deck.

The construction of five steel-fiee bridges in Canada (Bakht et al, 1998) enabled an accurate cost analysis to be performed. The first bridge constructed included a 6% increase in the tender price for the steel-free deck slab compared to the conventional reinforced concrete deck slab. However, in a subsequent tender, the lowest bid quoted was for the FRC bridge deck. The paper also described a NLFEA method developed by L/fufti and Wegner but concluded that accurate comparisons with experimental work can only be achieved after 'tuning' the parameters and this required prior knowledge of the experimental results

The ex7ensive research into compressive membrane action in bridge decks in Canada appears to have yielded a beneficial solution. However, the differences in both the form, the type of loading and the analysis used for bridge construction limit the use of such bridge decks in the UK; particularly in Northern Ireland where the use of steel composite bridges is less prevalent.

3.9 Other research centres

A major contribution to work into the effect of the edge restraint in restrained slabs m-as made b\, Guice and Rhornberg (1988) in the USA. These tests represented some in a limited number 0-f tests which measured and varied the edge restraint In 1990 Fang et al presented the results of field tests on steel con~posite beam-and-slab bridges The NLFEA package, SAPIV, modelled the arching phenomenon in two layers of finite elements and the analysis shoued reasonable correlation with the deck detailed under the Texas design code (an Ontario-type deck detail) It was also noted that the behaviour of the deck was essentially linear up to three times the current design wheel load A subsequent paper by Fang et a1 (1994) provided the results of tests on eighteen slabs with two supporting edge beanis

Azad et a1 (1993) carried out field test on the punching failure of composite beam-and-slab type decks in Saudi Arabia and found that the orientation of the crack width was critical to the ultimate strength. A subsequent paper ( h a d et al, 1994) described the interaction of flexure and shear in punching and compared the results of twelve '/2 scale bridge models with several theories The ACI predictions of the strength were highly conservative but the ATFEA gave good predictions Petrou and Perdikaris (1996) presented a theory similar to Rankin's approach A three-hinged compressive stmt with finite edge restraint was used to model the arching behaviour. A linear elastic FEA incorporating 8-noded brick element was used to establish the value of restraint.

3.10 Review of dynamiclfatigue load tests

The majority of research carried out and sumniarised in tlis report has been for static load However, as the live loading on a bridge is dynamic the following section outlines some of research carried out with cyclic and rolling wheel type loads. One of the most influential series of tests was carried out by Batchelor et a1 (197Sb). From the numerous results they obtained the following relationship between the fatigue load and static failure load, where N is the number of load cycles

This suggests that a load which is a fraction of the static failure load, such as the working bridge load, needed to be applied for a large number of cycles to have any significant effect In their tests the nun~ber of load cycles varied between one and five million

Fang et a1 (1990) carried out tests on full-scale bridge models which incorporated fatigue tests. A fatigue load of between 22kN to 115kN was varied sinusoidally and up to 5 million cycles of load applied. The same year Jackson (1990) referred to dynamic testing of bridge models in the UK. He highlighted the greater effect of a rolling wheel load compared to a pulsating wheel load. In Jackson's test, the rolling wheel load was applied for 5000 cycles Moussard (1993) carried out dynamic tests on HSC specimens where two million load cycles of 100kN load were applied at a frequency of 1Hz. He concluded that a dynamic coefficient of 1 3 was required for comparison to static tests

The hlinistry of Transport in Ontario, have carried out numerous dynamic tests on both full and part-scale models. In 1995 Bakht described tests conducted on third scale models, in which the cyclic load was varied from OW to 40kN and applied for two million cycles. In 1995 Selvadurai and Bakht provided information on tests simulating a rolling wheel load on a hll-

A gitrde to comyressi~v nzemhmr~ nciior2 irl bridge deck slobs 12

scale FRC deck They adopted Perdikaris's method of simulating a moving wheel load mhich used a sequence of pulsating loads. A frequency of 3Hz was equivalent to a wheel moving at 40krn/hour The deck slabs xvere siniilar to the fibre-reinforced slabs pioneered in 1993 by Mufti et a1 and contained 0.88% polypropylene fibres. The decks behaved adequately under four million passes at 98kN loading

3.11 Summary of methods

The review of literature presented an oven~iew of the various methods for predicting t l~e enhanced strength of laterally restrained reinforced concrete slabs. The methods can be categorised as hand-calculable elastic-plastic and plastic with non-linear finite element analyses (NLFEA) being a computer based elastic-plastic method. Table 1 (p.27) summarises some of the reported methods under these three categories.

The NLFEA computing techniques used to model arching action require both non-linear material and geometric properties. Although the technology in this field has advanced greatly in recent years, the programmes are overly complex- for the vast majority of bridge designers lo use. Additionally, many of these NLFEA have been performed for slabs where the strengths are known. This has often involved calibrating the model and in many cases the NLFEA parameters differ for each experimental test model beins simulated. In this respect, it is not feasible within the scope of this guide to summarise a NLFEA method for predicting the strength of laterally restrained bridge deck slabs.

The plastic or yield line methods have generally developed from the work by Wood (1961) and Park (1960 & 1980) Most methods require some mathematical manipulation which leads to long expressions. The method proposed by Eyre (1994) predicts a safe load as opposed to an ultimate load and the factor of safety is unknown. Eyre's method also assumes rigid restraint which may not occur in structures in practice. For simplification and due to the similarities in most of the plasticity approaches, the method by Park (19'80) has been presented in this design guide

The elastic-plastic approach is typified by the Queen's University of Belfast method. However, some of the approaches, such as Brotchie (1963), do not account for a varying amount of external lateral restraint. Christiansen's semi-empirical method separates the arching and bending phenomena This is similar to the method derived by Rankin and Long (1997) at Queen's University which has been presented in this design guide

1.8 Srrnmmarg: of methods for pr-edictillg the strength of Eaterally restrained bridge deck slabs

1.1 Introduction

In this section. an ovewiew is given of the various methods for predicting the strength of iaterally restrained slabs Some distinction has been made between the type of analysis used The University of Canterbury's (Park and Gamble, 1980) method has been used to demonstrate a plastic approach and the Queen's University procedure represents an elastic-plastic method Using the Queen's approach, the possible modes of failure for a bridge deck slab are established and a distinction is made between the flexural and shear punching modes of failure.

4.2 Comparison to the existing code (BS5400)

In the British Standard, RS5400 (1990) and associated BD's, a bridge structure is designed to resist the worst combination of HA, a uniformly distributed load representing normal traffic in the UK, and HB loading, an abnormal vehicle unit loading in conjunction with other superimposed loads such as wind and temperature The design code applies five separate load con~binations each comprised of other load combinations and envelopes. However, as discussed in Section 2, the predominatins criterion for the design of the deck slab is the local effect under a concentrated wheel load. In BS5400, the bendins capacity is described by the following equation (with the safety factors removed):

The equation has been used to predict the flexural strength of the Taylor et al's (2001a) tests on one-way spanning slab strips. As highlighted in Table 2 (p 29), the predicted values are highly conservative for laterally restrained slab strips and are increasingly conservative at high concrete compressive strengths This is demonstrated graphically in Fig4

FE - fixed end S/S - simply supported LiR - lateral restraint K = stiffi~ess of end restraint

0 2 0 4 0 6 0 80 100 120

Concrete Cube Strength (Nlmrn2)

Fig.4: Comparison of slab strip fzilmre loads to predicted values in design code

The test results clearly show an increase in ultimate strength nith increasing concrete compressive strength but this is not recognised by the d e s i ~ n code The test results also demonstrate the increase in ultimate strength with an increase in the lateral restraint. This is also neglected in the current code methods Conversely, the desisn code, with safety factors removed, accurately predicts the strengths of the simply supported test models. A second series of tests on bridge deck models has also been used for comparison (Taylor et al, 2001b) with the current design code These tests were aimed at more realistically modelling the restraint conditions in a real bridge deck slab by incorporating the supporting edge beams. The supporting beams act as external restraint to the slab and by varying the width of the edge beams the stiffness of the external restraint was varied. In order to relate the applied bending moment to the flexural moment capacity, the relevant Pucher chart was utilised to assess the effects of the concentrated load (similar to the local wheel load). This gave a relationship of applied load to bending moment of

The punching shear strength is given in BS5400 by the following equation

The critical perimeter is assumed to be at a distance of I 5d fiom the edge of the loaded area. A sumnary of the predicted ultimate flexural and punching shear capacities is given in Table 3 (p.29) and some of the results have been presented in Fig. 5 The test results clearly show an increase in ultimate strength with increasing edge beam width which is equivalent to increasing the external lateral restraint stiffness. This is not recognised by the BS5400. It can be concluded that the current British codes do not accurately predict the strengths of the model deck slabs and in reality there is a substantial enhancement in both the flexural and punching shear capacities due to Compressive Membrane Action

trendline. P"P

/ /-

/

BS5100 (flexural mode) -- -- -- -I 0 I I I

50 1 00 150 300 750

Supporting edge beam width (rnm)

Fig.5: Comparison of 113-scale model bridge deck slab failure loads to predicted valares in design code

A mi& fo comvre~sr l~e r ' m ~ ~ h r ~ m e nctrm rrz br-idye deck slobs 15

1.3 Qrreen9s University af Beffast approach

4.1.1 Kirkpatrick, Rankin arrd Long

Kirkpatrick et a1 (1953) developed a simple means of assessing the punching capacity of reinforced concrete bridge deck slabs by considerins arching action They assumed that a bridge deck has an effecti17ely rigid restraint system and the mechanism of failure is a punching shear mode Kirkpatrick believed that the diapliragms in his own tests had provided the necessary restraint to prevent the transverse movement of the beams due to the arching thrust The design charts derived by Kirkpatrick are illustrated in Fig.6

4 8 12 75 20 2 i 2 8 32

L/h

Fig . 6: Kirkpatrick maximum arching moment carves

The design charts were used to establish the maximum arching moment in terms of the concrete compressive strength and the span to depth ratio where.

RI,, = k f , . hZ and k = N . R i , ( Mr = 4 for rigid plastic material rEqn.21 4 <4 for elastic-plastic material)

When the maximum arching moment has been calculated it can be related to the equivalent area of flexural reinforcement, p,, using the following.

p, = kf,. hz [Eqn.8]

240d2

This was than substituted into Long's (1975) equation for the shear punching strength i.e: for a circular load:

Ppt =1.52.(++d).d.&.(100~,)"" I%n-91

or more generally described by:

u here rt; shape factor = 1.0 (circular load) or 1.15 (rectangular load) and critical perimeter is taken at 0.5d from the face of the loaded area.

.-I mide lo contpres.sr~e n7embrzrlte crctio~z in bridge deck slabs 16

However the archmg capacity cannot exceed the maximum capacity as represented in Fig 7 and by the following equation

ann = Id2

Fig. 7 : R/Lar;irnum arching capacity of a slab

Kirkpatrick et al's method showed good asreement between predicted and actual failure loads for several reported tests on bridge deck s ldx However, the predictions were slightly unsafe where a flexural failure occurs, such as in lightly reinforced slabs with a moderate degree of external lateral restraint In this case the following refinements were developed

4 .42 Rankin and Long

Rankin and Long (1997) first developed their approach for the strength of laterally restrained slab strips as part of their rational approach to predicting the enhanced punching strength of slab and column specimens The method separates the bending and arching components In reality the two mechanisms are combined and the compression in the concrete is due to both the action of arching and bending. Rankin extended the theory of McDowell, McKee and Sevin (1956) which focused on the geometry of deformation of laterally restrained masonry walls Two non- dimensional parameters, R and u, are used to describe the geometry of deformation.

'R' is a measure of the elastic deformation and 'u' is a non-dimensional measure of deflection of the slab strip. Rankin mathematicaIIy manipulated these terms to derive expression for the arching moment ratio where.

( i ) R > 0.26: RZ, = 0.3615 and u = 0.31 (constant) [Eq n. 131 R

the an

( i i ) 0 < R < 0.26: M = 4 . 3 - 1 6 . 1 d 3 . 3 ~ 1 0 - ~ + .IBGR 1'

~1 = - 0.15 + 0.36 J0.18 + 5 . 6 R [Eqn.l-%]

In predicting the arching strength of restrained reinforced concrete slabs it is, therefore, necessary to establish the depth of the arching section, ?dl, and the plastic strain value, E, The depth of section available for arching is firstly estimated from the overall depth minus the depths of the con~pression zones due to bendins The plastic strain value is the value of strain uhen hi1 plasticity is first achieved This was established using an equivalent trapezoidal stress block %here the base length of the rectangular portion is equivalent to F times the ma~inium strain value (Fig 8) The value of the plastic strain is then given as

sC = 2 ES. ( I - P ) [Eqn.lS]

Fig. 8: Eqrrivalent stress conditions zt ultimate b a d under proposed methad

The strength of laterally restrained slabs is highly dependent upon the degree of external lateral restraint Therefore, the restrained slab system with finite restraint stiffness was equated to a rigidly restrained slab, i e infinite stifiess, using the three-hinged arch analosy as discussed in Section 3.4. The solution to the equilibrium equation is outlined in Appendix B of Rankin's thesis (1982). In summary, the longer equivalent rigidly restrained slab has been used to describe the load-deformation response of a shorter finitely restrained slab. The equivalent length is then given b y

A grride to conipressi~v menibrnne nctiori ill brigye deck slabs 18

T h s provided a simple analytical expression 11-hich could be incorporated into the non- dimensional parameters used to describe archiny moment. The stiffness of the slab strip has been based upon the axial stiffness where

K = E,AIL, where A = a. 4 per unit width, and Er = 4.23 fCtto' [Eqn.l7]

'A' is the depth of the contact zone as described in Fig3 and the \value for the elastic modulus has been based upon Hognestad's (1956) relationship. Hence, a means of obtaining the arching moment of resistance for a slab strip with finite lateral restraint had been achieved Howe\.er, both the length of the equivalent rigidly restrained strip and the contact area are dependent upon the degree of lateral restraint and this method requires an iterative process to determine a constant value of dl To save mathematical iterations Rankin and Long (1997) suggested that it is usually sufficient to approxin~ate 'A' as half the depth of section available for arching, d l , times the width

4.4.3 Taylor, Rankin and Cleland's approach

The British Standard, BS5-100, assumes one value for the ultimate strain and describes the parabolic stress block by an equivalent stress block equal to 0 . 9 ~ (Fig 10). It has been proven that the value of ultimate strain changes with concrete strength and a report by the Concrete Society (1999) proposed a series of stress-strain relationships for concrete with varying compressive strength up to 115~1rnm~. The stress-strain relationship was used to develop an equivalent rectangular stress block Taylor et a1 (2001a) have outlined the adaptation to the n-~aterial properties to incorporate both normal strength concrete WSC) and high strength concrete (HSC) The variation in the ultimate strain can be represented by the following equation

E,, = 0.0043 - [ &, - 60)'2.5 x I o - ~ ) ] [Eqn.24]

The depth of the stress block is also given by:

p = 1 - 0.O03fcu

where p is the depth of the equivalent rectangular stress block as a fraction of the depth of the neutral axis from the compression face, x (Fig. lo).

'+ BSj4OO proposed

stress stress

block block

Fig.10 : BS5400 conditions at ultimate flextrral load for SSC (fr,< 6 0 ~ 1 r n r n ~ ) 2nd proposed stress block

A YIIICJC fo CO~IJ; I I 'C .S . .T~I~C n w n ~ h m m n c f r o r l i i l br.i&e deck slabs 19

The method outlined in the previous section predicts the enhanced flexural capacit), of laterally restrained slab strips but is not directly applicable to the punchins strength of bridge deck slabs A means of assessing the degree of lateral restraint inherent in such a system is critical to the prediction and in the past this has not been achieved satisfkctorily. It has been established that the ~bidth of the edge beams had a significant influence on the ultimate strensh of the slabs tested by the authors (Taylor et al, 2001b) This has been clearly demonstrated in (Fig 5) By equating the bending of the wall support to a hypothetical spring of an equivalent stiff~iess in the analysis of the strip tests by Lahlou and Waldron (1995), accurate predictions of the failure loads were achieved It seemed reasonable to employ a similar hypothesis for the bridge deck slabs The refinement proposed by Taylor (2000) used a model restraint system where the supporting edge beams, end diaphragms and surrounding area of unloaded slab were equated to a spring of an equivalent stiffness (Fig. 9).

b = effective nidth 5 loaded slab -

\ supporting edge bean nidt h

L L deck slab

e\teriial restramt

Fig.9: Restraint model proposed by Taylor (2000)

-

It \&as estimated that the influence of the arching force was sufficiently low at a distance equal to the effective span plus the depth of the slab (LC + h) from the face of the support This observation agreed with others' findings, such as those by Fang et a1 (1994) Initially the value of external lateral restraint stiffness was used in an elastic-plastic method for a two-way spanning slab with the elastic and plastic moment factors ascertained from a finite element analysis and yield line analysis respectively. The method, as outlined in Chapter 7 of Taylor's thesis (2000) was cunlberson~e and takes considerable effort A simplification to the method to facilitate its use by designers m-as considered to be of primary importance

b

A hndamental simplification in the preceding analytical approach was the assessment of the degree of lateral restraint by a 'restraint model'. This gave reasonable predictions for the strength of the bridge deck nlodels tested and the restraint model provided an adequate basis for a simplified approach A t)lpical bridge deck restraint model is illustrated in Fig 9 An effectiire ~vidth of slab subjected to arching forces can be described by

b e e c, + 2.L, + 2h (where LS=L/2 - c,/2) [Eqn.l8]

This corresponds to a slab axial stiffness of

The edge beam equates to a spring of equivalent stiffness and has an equivalent axial area described by (as derived in Appendix 7.1 of Taylor's thesis).

3 Ab=.r.Le.13 b/ beff

= constant for support conditions of edge beam = 550 (most bridges) [Eqn.20]

xvhich equates to an axial stiffness of

If the area outside the effective width acts in parallel to the end diaphragms in resisting the outward arching thrust, the areas are cumulative and can be summed to give a total effective area, Ad, where:

Ad= area of diaphragms + area of slab outside the effective width

However the stiffi~ess of the edge beams act in parallel, as opposed to additionally, to the diaphragms and it is the flexibilities of the system which accumulate to give an overall lesser restraint than each component as given by:

or K,= 1/(11 Kb + 11 Kd ) [Eqn.23]

Hence the ratio of restraint stiffness to slab stiffness is calculated by (K,/ Ks) derived from the previous equations By use of the restraint model, Rankin and Long's (1997) integrated procedure was then directly applicable. However, the material properties and tests used to validate this theory were based upon concrete with cylinder compressive strengths up to 70/mm2 A modification to the stress-strain relationship to incorporate concretes with high compressive strengths (>70/mrn2) was considered.

A refinement to determining the shear punching capacity of a slab with less than infinite restraint was also established by utilising the arching capacity determined from the 'restraint model' method Similar to Kirkpatrick et al's (1934) approach, an 'equi\ra1ent7 area of reinforcement was estimated by using

This quantified the shear punching strength in terms of the equivalent area of reinforcement due to the combined effects of bending and arching i.e.:

0.43 Pp, = --vE.(criticd perimeter).d(lOOpt)a'I [Eqn.27]

5 where rf, shape factor = 1.0 for a circular wheel load and critical perimeter is taken at 0.5d from the face of the loaded area. For con~parison with test results usins a rectangular patch load rf =

1 15. For pneumatic tyred vehicles, it is unlikely that stress concentrations would occur, therefore rr = 1 0 would be satisfactory

The tno-phase approach predicts an ultimate strength awarding to the lesser of the flexural and shear punching mode predictions i e

The following flow chart illustrates the steps to be taken in the calculation procedure for the flexural and shear punching strengths of laterally restrained slabs.

1. Effective mid th of loaded sEab 1

1 3. Bending Capacity I

4. Arching Section I

1 5. Equivalent rigidly restmined slab

1 9. Arching Capacity

w

1 11. Shear puncfling capacity 1

I / 12. Ultimate capacity

Repeat u n t ~ l constant

, \ d u e of a

The subsequent equations present the detail of the procedure proposed by Taylor (2000) for predicting the ultimate strengths of a laterally restrained bridge deck slabs,

Effective width of loaded slab:

Stiffness parameters :

E, = 4 23fc,," K, = E, A,l/L, IXb= ~ ~ ~ 1 1 2 or transformed I-beam &= < L? I,d be$ where < = constant for support condition < =114 5 (SIS) or 985 (FE)

Kb = Ab E J Le .Ad= area of diaphragms + area of slab outside the effective width Kd =C &.El L, K T = l / ( l / K b + I / & ) ) K, = E, h.b,&e

3. Bending Capacity :

Depth of stress block, P = 1 - O.OO3& but < 0.9 - uepth of neutral axis, x = J . As

0 67.fcuP b Lever arm, z = d - 0 5P x Mb = A. A,.z Pb = kb.Mb

4. Arching section

2.dl = h - 2x.P New dl from previous iteration

5. Afine strip

A = a.b.dl and L, =L,

6. Arching parameters E, L;

E~ = 0 0043 - [( f,,,- 60) 2 5 x lo-'] but < 0 0043 and R=- 4 d?;

Ecz2Eu(1 - p ) 7, Deformation

R > O 2 6 u = 0 3 1 (constant)

8. Contact depth a = 1 - u/2 2 ad1 use for refined arching section above until value remains constant

9. Arelming capacity

X i , - 0 168.b,fc,, dl2 h/l, (LJL) [For maximum arching L, = L, 3 Ma, = 0 1 6S.fc,, dl' hl , ]

10. Flexural prrnchirtg capacity

Pa + Pb

1 1 . Shear punching capacity

critical perimeter at 0.5d fi-om face of loaded area

12. IJltimate capacity

A worked example for the proposed method is given in the Appendix. A spreadsheet I\-as adapted for this procedure and has been used to compare the predicted values with several tests carried out on bridge deck models as shown ill Tables 3, 4, & 5 The method has also been compared with Kirkpatrick's earlier method in Tables 3, 4, & 5 In Table 4 it can be seen that the flexural failures exhibited due to the low external restraint stiffness were not accounted for in Kirkpatrick et al's n~ethod

4.3 Bark's method

Park has been one of the major contributors to research into compressive me~nbrane and uses a plastic theory for the load-deflection behaviour of a restrained strip at ultimate load The following procedure is outlined in Chapter 12 of Park and Gamble's book (1980). A fixed-end strip with plastic hinges is depicted in Fig.1 1 with partial lateral restraint allowing an outward displacement of 't' at each end The section of the slab strip between the hinges is assumed to remain rigid.

Fig.11: Park's plastic hinges for a restrained slab strip

.4 gl/ide to compressive mt?rnbrarvi? actiolr in bridge deck slabs 24

Park also assumes that the sum of the strains have a constant value, E, along the length of the strip Referring to Fig. 12, the shortening in the middle section is, ~(1-2B)L, giving a total lensth of portion I -2 as shown.

Fig.12 : Park's geometry of slab strip portion between yield line sections 1 - 2 above

From equilibrium of forces, the following expressions for the membrane force and the moment of resistance were developed

The sum of the moments at the yield section about the mid-depth was expressed as:

By considering strain con~patibility, equilibrium at the section and by equating the work done at the yield sections with the ~ i r tua l work done by the load, Park obtained an expression for the load, dependent upon the central deflection, 6 The terms required to develop this expression are lengthy and the procedure has been simplified by means of a spreadsheet. An example of slab strip S5 tested by Taylor et a1 (2001a) is summarised below and the comparison to the full test series is given in Table 2 The following variables are considered.

1 .Stiffness parameters: Concrete elastic modulus, E, = 4 23 x 10 1 l o = 42 531<r\Umm2

Slab stiffness, K, = 42.54 x 475 x l50/7 12.5 = 4254kNlmm

External restraint stiffness, K, = 197hT/1nm (measured) K, = 4 11.74N/mrn per mm width

2. Forces:

From ACT code C, = 0 85f c p 1 c where Dl= 0 85 for f ', <30Nimm2 and reduces by 0 008 for each unit increase but > 0 65

p,= 0 85 -[(SO 9 -30)0.008]= 0 62 ... p1= 0 65 For unit uidth. As=O 7lmm?/mrn ST = 0 71 u 500 = 356 S4N/mm For consewative approach assume T = C, , :. T = T' = C', = 3 56 83Nlrn1m

3. Strain value a ~ l d !eve[ of neeitrd axis

Assume 6 = 0 311 = 5 0 m l for example [note 'D' used for '6' in spreadsheet]

TI-T - C', +CL 2 4 46 1 .7fvc P,

11,,6 = (C, + C, -T)6 =OSSfc p l c 6 = 0 8 5 v SO9 v 0 6 5 ..: 3477 .r 50=77691N mm/mm n1,, = 0 S5fc Pic (0 5h-0 5Plc) + C,(O 5h-d') +T(d-0 5h)

= 0 85 x 80 9 x 0 65 x 34 77(O 5x150 - 0 5x0 65x34 77) + 356 S4(O 5x150 - 16) + 356 84(104- 0 5x150) = 1 19677N mdrnm (from symmetry m,, =m',,)

4. Energy prinacipal :. (PI2 x L/2.)8 = (mu + m', - nu 618 (P/L)/4 = 119677 + 119677 - 77694 = 161660Nmm per unit width

= 76.79 KN.m for slab strip 3 P = 76.79 x 411.415 = 217.lk;V (at 6 = 50rnm)

The procedure is repeated at various values of deflection to find the peak load. The graph of load versus deflection is then plotted (from the spreadsheet in the - Appendix the peak load was found to be 23 1 9kN) Thus;

Ratio test/predicted load = 192/231.9 =0.83

A gzude to compre.ssive rnembrme nctiors in bridge deck slabs 2 6

5.0 Cancluding remarks From the review of literature and from the summary of the proposed methods for predicting the strength of laterally restrained slabs, a primary conclusion to be drawn is that bridge deck slabs have strengths far in excess of those predicted by conventional design methods which are based upon conventional flexural theory and empirical shear strength equations for unrestrained slabs. The use of Pucher charts or Westergaard's equations, as recommended by BS5400, underestimated the ultimate strengh of laterally restrained bridge deck slabs as they take no account of the in-plane forces set-up as a result of Compressive Membrane Action (CMA).

CMA has a more significant effect on the strength of laterally restrained slabs with low span to depth ratios. As the span to depth ratio of bridge deck slabs is normally less than fifteen, the strength of these slabs is considerably enhanced CMA is also strongly influenced by the degree of lateral restraint. Lateral restraint is inherent in bridge construction in the form of edge beams, end diaphragms and the surrounding area of unloaded slab. It has been demonstrated that the strength of the laterally restrained slabs also increases with increasing concrete compressive strength This gave a higher degree of conservatism in the predicted strensths of the high strength laterally restrained slab strips, using standard flexural theory. Consequently, the utilisation of the arching phenomenon in high strength concrete bridge decks has the potential for producing substantial economies in beam-and-slab bridge decks.

The methods based on arching theory gave more accurate predictions for the strength of a wide range of laterally restrained bridge deck type slabs compared to the current codes The Queen's University of Belfast approach gave more consistent and slightly conservative predictions compared to the highly conservative predictions using the code The plasticity approach developed by Park at the University of Canterbury, Xew Zealand, also gave more accurate predictions than the current code However, the predictions were slightly unsafe compared to the ultimate strength of slab strips tested at Queen's University (Table 2)

The drafi Departmental Standard, BD81101, has partly addressed the use of CMA for the design and assessment of bridge deck slabs in the UK; although it does not address some of the limitations to its use; such as the boundary restraint and particularly its requirement for intermediate diaphragms. The draft BD8l is based on the Queen's University of Belfast approach which has been validated by hl l - scale testing of real bridge deck slabs. Future in~provements in this approach could be that the limitations may be reduced if flexural punching failure is taken into account The approach would then encompass punching in slabs with a relatively low degree of external lateral restraint.

One of the barriers to the use of compressive membrane action has been the complexity of the calculations required. This report has addressed this issue The second barrier is the accurate estimation of the effective stiffness of the external restraint in real slab systems, such as bridge deck slabs. Based upon tests on reinforced concrete bridge deck models, a method for evaluating the level of ex7ernal restraint stiffness was established. However, the method has been validated by only a small number of tests and krther tests on bridge deck slabs with varying geometry and on steel composite bridge deck models may further endorse this method Recognition of CMA in bridge deck slabs through the adoption of the proposed BD81 could lead to many innovations in the way in which future deck slabs can be reinforced This should lead to less reinforcement and increased cover, giving more econon~ical and durable concrete bridge deck construction

Table I : Categorisatton of methods for predicting the e~rlzanced strength of restrained slabs

Category Authors Year

H;and-cakalable elastic-plastic

Csnrperter based elmtic-plastic (N LFEA)

Ockleston 1956

Brotchie 1963

Liebenburg 1966

Christiansen and Frederikson 1963 & 1983

McDowell, McKee and Sevin 1956

Long, Rankin, Kirkpatrick, Taylor & 1975-present Cleland (Queen's)

Wood

hlorley et a1 (Cambridge)

Braestrup

Kemp and Eyre (City College) 1967-1993

Park 1960-3 980

Cope, Rao and Clark

Morley et a1 (Cambridge)

Jackson 1987- 1990

Bakht, Jaeger, Mufti, Agarwal and 1980- 1998 Thorburn (Canada)

Lahlou and Waldron 1992

Fang et a1 1990 & 1994

Azad et a1 1993 & 1993

Petrou and Perdikaris 1996

.4 gttrde fo conrpressi~~e membrme nctior~ i r z bridge deck slabs 2 8

Table 2: Comparison of ultimate strengths of one-way slabs tested at Queen's University (Taylor et A, 20012) with those predicted by British design code, proposed Queen's method and Psrk's method

Model Reinforce- J E , PT Pns, PtRm P, P-rRp ?park PtPp, ,~ No. ment ( ~ l m m ' ) (W) (I&) (kN) Om

05%T&B 1 1 2

0 5%T&B $0 8

0 j%T&B 61 5

0.5%T&B 82 2

C).5%T&B 101 1

0 5 % B 318

0 5% B 91.0

0 5 % B 100 1

0 5%T&B 89 3

none 90 5

0 5% centre 96 8

Oj%T&B 1010

fibres only 104.9

0.5%T&B 39.5

0.5%T&B 60.9

Average = 2.03

* '514 span loading T = top layer of reinforce~nenr R = bolt0111 layer of reinforcement F/E = fixed end LR- longitudinally restrained SIS- simply supported !I= 17 mil1

Load. PkN

I I 1125mm clear span I i 91

Table 3: Comparison of d t imate strengths of bridge deck s h b s tested c2t Queen's Urriversity (Taylor et al, ZOOlb) with those predicted by British Standard, proposed Queen's method and Kirkpatrick's method

D3 65 0 0 - 0 0 - 4 6 6 1 3 9 -

D74 6 5 0 0 - 0 0 - 43 6 1 4 8 - -

D5 150 38 0 3 91 83 4 1 SO 151 1 0 99 268 0 0 56

D6 182 38 1 3 78 84 4 2 16 173 3 1 05 276 1 0 66

D7 135 3 8 1 3 5 4 8 5 1 1 5 9 9 2 5 1 4 6 2 8 0 9 0 48

D8 157 3 8 7 40_5 8 4 7 1 1489 1 057740

A\.erage 4-02 1.86 1.19 0.57

St. deviation 0.20 0.06

Coeff. Vsr. 0.168 0.101

25x500 loading plate

Tests by Taylor et al(2001b)

Table 4: Comparison of test results by Kirkpatrick with predictions using two methods

Test Panel Pt P, Pt/Pp Pkrk B t / P i h h

No.

A1 102.5

A2 114 0

A3 102 5

A4 108.0

A5 96.0

B1 108 0

B2 96.0

B3 100.0

B4 90.0

B5 91.0

Cl 106 0

C2 100.0

C 3 102.0

C4 1100

C5 105.0

D l 98 0

D2 108 0

D4 118 0

D5 107.5

Average

St. deviatioa

Coeff. Var.

Beams 1 50mmx450mm deep

Tests by IGrkpatrick, 1884

.4 ailide to con~ures.si~.e rnenlhrmre ncfiorz irr bridge deck slabs 3 1

Table 5: Comparison af test results by Bafchelar et a! with predictions using two methods

R'lodel NO. Pt Bp Pt/pp P ~ r h P t m ~ r k

5 A3

5B3 5 c; 7C1

SCl

5A4

5B4

5C4

A\.erage 2.04 0.89

St. deviation 0.11 0.16

Cocff. Var. 0.012 0.177

Channel 3 76OmmcIc L=2Xrum b,:~3O?mm loading shoe 95 s 631nm elhpse (equlr alelit circular drameter of [(63+95)/2 + d] used for critlcal perimeter)

Tests by Batchelor et al, 19'78

-4 gurcle to compres.wse r~re~?ihrme action 11.1 reinforced concrete bridge decks 3 2

Example for predicted strength of a typical bridge deck slab. Assuming: - 350mm x 750mm rectangular supporting beams

- bridge span = 13m (has negligible influence on the slab design)

. . : . equates to : : . . . . / 2.0111

7

of width, b S ~

Fig.Al: Typical bridge deck slab

EXAR~PLE 1 : Slab variables: d = lOOmm L e = 850mm berY = 2300mm (as below) f , = 4 6 0 ~ l m r n ~ h = 150mm , = 4 0 ~ i m n 1 ~ L = 2000mm A,= 1 . 0 % = 2 3 0 0 m 2

Note: clear. spa^ taken as 2. On?)

2 . Effective width

2. Stiffness parameters :

3 . Bendir~g Capacity :

Depth of stress block. = 1 - (0 003 x 40) = 0 88

Depth of neutral axis, x = 460 x 2300 = 19.51mm

0 6 7 ~ 4 0 x O 8 S x 2 3 0 0

Leverarm, z= 1 0 0 - ( 0 . 5 ~ 0 8 8 ~ 1 9 5 l ) = 91 43nm

hlb = 360 s 2300 s 91 42 s lo-" 96 72kN m

For fixed end Pb = ( 8 L ) Mb = 386.9kN

4. Arching section

2.dl = 150 - (2 x 19.51 x 0.88) 3 dl = 57 84

5. .&Em strip

Assume a.= I for first iteration

A = 57.84 x 2300 = 133032mm2

6. Arching parameters

E,, = 0 0043 - [(40-60) 3 .5 x lo-'] = 0.0048 < 0 0043? use 0 0043

r, = 2 x 0.0033 ( I - 0.88) = 0.00103

7. Deformation

8. Coratact depth

a = 1 - 0.27112 = 0.865 3 ad1 = 50.0

Use for refined archin,o section and steps 3 - 7 repeated give

A = 1 15000mm2 = 1588mm

E, = 0 0048 > 0 0043 use 0.0043

E, = 0.0013

R = 0 1935

O < K < O 2 6 = > u = O 2 5 6

a = 1 - 0 256'2 = 0 872

ad1 = 5 0 4

Cse for refined arching section and steps 4 - 7 repeated @\re

.4 guide to cornpre.~si~.e 17ienrbrcme nctiori in reirgorced concrete bridge & c b 3 4

A = 1 l592Ornrn2

L, = 1592mm

E, = 0 0048 > 0 0043 use 0 0043

E,= 0 0013

X = 0 1955

0 < R < 0 2 6 = u = 0 2 5 6

a = 1 - 0 25612 = 0 872

a ad1 = 50.4 same value as previous hence use these values

9. Arching capacity

O < R < 0 . 2 6 h4 =4.3-16,1,/3.3x10~'+0.1243x0.1955 = I 7 7 3 3

10. Flexural punching capacity

PPf= 386.9 + 97.9 = 484 SkN

1 1 . Shear punching capacity

13 Ultimate capacity If PPf < P,,. 3 P, = P,r If P,f > P,, =3 P, = P,,

2 P, = 414.5W (shear type faiture)

EXAMPLE 2 : Slab variables: as Example I except As = 0.5% = 1 150mm2

1 . Effective width (as before)

2. Stiffness parameters : (as before)

3, Bending Capacity :

Depth of stress block, P = I - (0.003 x 30) = 0 88

Depth of neutral axis, x = 460 x 11 50 = 9 75mm O 6 7 x 4 0 x O 8 S x 3 3 0 0

Lever arm, z = 100 - (0.5 x 0.88 x 9.75) = 95.7mm

For fixed end Pb = (SIL).Mh = 202.5kN

4. Arching section

2 d l = 150 - (2 x 9.75 x O.S8) 3 dl = 66.3

5. Affine strip

Assume a.= 1 ibr first iteration

A = 66.4 x 2300 = 1 52720mrn2

6. Arching parameters

,3? use 0 0033 E,, = 0 0033 - [(40-60).2 5 x = 0 0048 < 0 "0"

E? = 2 x 0.0043 (1 - 0.88) = 0.00103

7. Deformation

8. Contwt depth

a = 1 - 0 23712 = 0.882 z a d 1 = 58 6

Use for refined arching section and steps 4 - 7 repeated give'

A = 134780mm2

L = 1662mm

E, = 0.0048 > 0 0043 use 0 0043

E, = 0.00103

R = O 16155

O < R < O 2 6 = > u=0 .225

cx = 1 - 0 22512 = 0.888

3 a d 1 = 59 0

Use for refined arching section and steps 4 - 7 repeated give

A = 135700mm2

= 1665mm

E,, = 0.0048 > 0.0043 use 0 0043

r, = 0.00103

R = O 162

O < R < 0 . 2 6 = u = O 2 2 5

a = I - 0 22512 = 0 888

=i a d 1 = 59 0 same value as previous hence use these values

9. Arching capacity

0 < R < 0.26 M r = 4 3 - l 6 l & . 3 x l 0 ~ ' +0.1243x0.162 = 1.9958

Ma = 0.168 x 2300 x 40 x 66.42 s 1 9958 (85011665) x lo-' = 69 5kN m

P, =(4/L).M,= 139 OkN

10. Flexural punching capacity

PPf= 202.5 + 139.0 = 341.5kN

11. Shear punching capacity

12. Ultimate caprtcity

If PPf < P,,. =3 P, = P,f If P,f > P,,. z3 P, = P,,

The examples given can be compared to serviceability tests carried out on a bridge with similar diinensions in Northern Ireland. The test panel with an average of 4 2 ~ l m m ~ concrete compressive strength and 0.6% top and bottom reinforcement had a 3SOkN test load applied u-ith no adverse effects and a maximum midspan deflection of less than (spad700).

The two examples highlight the effect of reducing the percentage of reinforcement on a typical bridge deck type slab. The proposed method predicts a flexural type failure in the lightly reinforced slab compared to a shear type failure in the slab with 1% reinforcement The method also predicts a decrease in the ultimate failure Ioad of only 17% for a reduction in reinforcement of 50%.

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Guide to Compressive Membrane Action

This technical paper provides a concise summary on the use of

compressive membrane action in concrete bridge decks. It is

based on work funded by the Concrete Bridge Development

Group as part of its research programme.

Guide to Compressive Membrane Action Technical Paper No 3

First published 2002

O Concrete Bridge Development Group 2001

Published by the Concrete Bridge Development Group Riverside House 4 Meadows Business Park Station Approach Blackwater Camberley Surrey GU17 9AB UK Tel: +44 (0)1276 33777 a Fax: +44 (0)1276 38899

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Although the Concrete Bridge Development Group (limited by guarantee) does its best to ensure that any advice, recommendations or information it may give either in this publication or elsewhere is accurate, no liability or responsibility of any kind (including liability for negligence) howsoever and from whatsoever cause arising it, is accepted in this respect by the Group, its servants or agents.