Terminology
A"net contact area in longitudinal joints(in floor diaphragm)
A c"cross-sectional area of concrete
A f"cross-sectional area of flange of hollow core unit
A h"area of floor diaphragm reinforcement
A ps"area of prestressing tendon
A s"area of reinforcing bar
a"vertical deflection in a catenary system
B"length of longitudinal joints(in floor diaphragm)
b"total breadth of hollow cored unit
b eff"effective breadth of top flange in a composite beam
b v"total web breadth in hollow cored unit
b w"breadth of a single web in hollow cored unit
D"depth of hollow cored floor(in floor diaphragm)
e0"eccentricity to pretensioning tendons
E"Young’s modulus of concrete
F c"ultimate horizontal compressive force(in floor diaphragm)
f cp"effective compressive in concrete at neutral axis
f ctm"characteristic direct tensile strength of concrete(EC2)
f cu"characteristic28-day compressive strength of concrete
f pe"effective prestress in tendons after losses
f pu"characteristic strength of prestressin
g tendons
f t"characteristic28-day direct tensile strength of concrete(BS8110)
f y"characteristic strength of rebar
G "apparent shear modulus in floor diaphragm
h"depth of hollow core unit
h ct"depth of web with constant thickness in hollow core unit
h f"depth of flange of hollow core unit
I"second moment of area
J E"secant rotational stiffness where rotation of connection and beam are equal
K s"longitudinal shear stiffness(in floor diaphragm)
K s"ratio of rotational stiffness of connection to flexural stiffness of beam k"‘core’distance"I/0.5hA c(in hollow core unit)
L"span of beam
l"span of element in a catenary system
l p"transmission length of prestressing tendons l t"transmission length
M"bending moment
M add"additional design bending moment induced by deflection of column
M E"moment of resistance where rotation of connection and beam are equal
M h"horizontal ultimate bending moment(in floor diaphragm)
M R"ultimate moment of resistance of beam
M U"test moment of resistance of connection
N"axial force in reinforcing bar
P0"pretensioning force at release of jacking force
R"dynamic resistance of a catenary system
R a"roughness factor
S"first moment of area about a plane considered
v"transverse shear flow
V"vertical shear force
V b"maximum shear force in beam
V co"ultimate shear capacity of prestressed concrete flexurally uncracked section (BS8110)
V h"horizontal shear force
w"width of hollow core unit(in floor diaphragm)
y t"depth from top of section to neutral axis
"ratio of sum of flexural stiffness of column to sum of flexural stiffness of beam
"column effective length factor
"elongation of stability tie bar
s"longitudinal slip
t"transverse displacement,or crack width
ti"initial crack width between units in floor diaphragm
"average strain energy per unit displacement in bars measured at UTS "coefficient of friction
"diameter of bar,relative to beam}column rotation
sp"tensile splitting stress in prestressing transmission zone
zy"vertical web shear stress due to vertical shear force
zx"transverse web shear stress due to shear flow in the transverse direction
u"ultimate horizontal shear resistance in longitudinal joints(in floor dia-phragm)
Research and development in precast concrete framed structures
Kim S Elliott
University of Nottingham,UK
Summary
Research work on precast concrete framed structures carried out over the past20years has culminated with the large-scale testing of a five-storey frame in the USA,a pan-European project on the structural behaviour of frame connections,and the optimization of some highly engineered concrete elements.This paper reviews the most important advances,explaining to designers the relevance of the results of tests carried out on complete sway frames,on floor systems and connections subjected to gravity,horizontal and catenary forces,and on the wide-ranging developments of elements such as prestressed hollow core floor units.The design engineer now has more information,through full-scale experimental testing,realistic numerical studies and
3-dimensional nonlinear computer programs,to enable safer and more efficient design than ever before.
Prog.Struct.Engng.Mater.2000;2:405d428
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Fig.1Spectacular use of precast elements at Sabaf S.p.A.,by Martini Prefabbricati S.p.A.,Italy (Reproduced by permission of Martini Prefabbricati S.p.A.,Italy)[1]
1.Research on precast concrete framed structures
Precast concrete structures can be categorized as:E skeletal frames;E portal frames;E wall frames.
Of these,the skeletal frame is the most challenging,both structurally and architecturally,and has attracted the most attention in research and development.Since the 1930s,the skeletal frame has been transformed from its National Building Frame roots of heavy mass-produced elements,through its streamlined,long-span,lightweight period of the 1980s,to its present-day thermally and acoustically efficient maintenance-free structured form.In the year 2000,Zambelli [1]showed why precast concrete is considered by many to be the most versatile building material available (Fig.1).
Whilst portal and wall frames have limited application,e.g.warehouses,hotels,modular
apartments,the skeletal frame may be adapted for a wide range of multi-storey offices,car parks,
shopping/retail centres,schools and stadia }the main feature being the versatile use of large open spaces.The mass of structural concrete in a skeletal frame,is around 400}450kg m \2,or about 5%of its volume.
About two-thirds of this is in the floors,a fact which has led to a considerable amount of research and development on the optimization of pretensioned floors for both gravity and horizontal loading.With the avoidance of large quantities of wet in situ concrete being a major aim of the research work,prestressed precast concrete units provide us with one of the most economical flooring systems worldwide.
To remain competitive,precast structures must be erected quickly and with minimum site presence,particularly labour in high-salary countries.
Construction rates of 1000}2000m 2per week can be achieved with a fixing team of around six persons.To achieve this rate,the structural elements (columns,beams,floors and walls)must be erected simply and safely,through efficient connector design.The global stiffness of a precast frame is highly dependent on the local stiffness of the connections,often 5}10times that of the elements,as shown in Fig.2.It is vital that connections possess adequate strength whilst undergoing large deformations.
The most important connections in this respect are at the column }foundation and beam }column joints.Fig.2shows how sway deflections in an arbitrary three-storey skeletal frame vary according to:1.the ratio of the stiffness of the column to that of the beam;
2.the ratio of the flexural stiffness of the connection to that of the beam.
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Fig.2Effect of joint and member stiffness on sway deflections in skeletal
frames
Fig.3Precast concrete infill shear wall
The latter is clearly dominant.Accordingly research work has focused on the behaviour of connections,possibly at the expense of the beam and column elements,which have,in the main,been optimized in-house by the precast manufacturers.
The pejorative design rules that must be applied to precast concrete columns in unbraced frames (e.g.BS 8110:1985,Part 2,clause 2.5and EC 2:1992,clause 4.3.5.3.5)require that lateral bracing be used to stabilize skeletal frames of more than three storeys.Precast shear walls (Fig.3),cores,masonry infill walls,and cross-bracing,etc.provide lateral stability of different degrees of stiffness.In most cases,structural interactions take place between the bracing and the frame.As the global response is nonlinear,both materially and geometrically,it has fascinated academia,leading to widespread research work,
especially on the behaviour of infill frame walls,and on the interface shear capacity between walls,or wall and frame.
Unbraced frames are stabilized by columns acting as moment-resisting cantilevers,or if the designer so wishes,by frame action via rigid or semi-rigid connections.Customarily,pinned connections are preferred because of the perceived view that a semi-rigid connection could,if not properly detailed and constructed,soften at loads near ultimate failure.Pinned connections are easier to assemble,but rarely behave as perfect hinges because of the need for
continuity tie steel,which rather destroys the intended notion.Whether they behave in this way or not,unbraced frames have been designed mostly as pinned jointed sway frames.As a result,there has been little research and development on the global structural behaviour of precast sway frames until the 1990s,when a European research effort on semi-rigid frame connections [2]and the US }Japanese PRESSS project [3,4]made their impact.
Braced frames are stabilized laterally by
strategically positioned walls,cores or diagonal struts and ties.Because these elements often conflict with architectural requirements,their positions are often confined to stair and lift shafts,approximately
30}60m apart.The potential for ‘hot spots’of tension,shear or compressive stress concentration arise where the extraordinarily stiff bracing is connected to the flexible pinned jointed frame.Research has therefore focused more on the localized behaviour of such frames,particularly under cyclic or seismic reversals of load and/or large horizontal displacement.The need to develop hysteretic energy dissipaters has concentrated on attempting to satisfy the requirements of strength,stiffness and toughness simultaneously.Since the Ronan Point progressive collapse and other accidental or abnormal loading failures,a key issue for both designers and researchers has been the robustness of precast frames.Building insurance transactions have pivoted on ‘proof of structural integrity’as design engineers have sought means of enhancing the tenacity of structures.The so-called ‘alternative load path’method was proposed as a means of bypassing damaged elements or
connections.The much favoured ‘stability tie’method provides sufficient tie steel to ensure that,in the event of a loss of local stability,a new state of equilibrium is achieved by catenary action.Recent research work
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carried out on isolated connections or elements has not led to amendments to these rules,established around 1973,mainly because of the absence of full-scale frame testing needed to validate the isolated test data.The proposed construction and subsequent testing of the seven-storey(?)precast frame at BRE,Cardington,UK is eagerly awaited.
Although the market share in the UK for precast concrete is only about5%of all multi-storey framed buildings,and for precast floors is around40%of floors used in every type of building,the research effort on structural precast concrete does not mirror these facts.In a survey carried out by the author (1996}98)on behalf of the FIB Commission on Prefabrication(International Federation for Structural Concrete,formed in1999by amalgamation of FIP and CEB;contact fib,Case Postale88,CH-1015Lausanne, Switzerland.E-mail fib@epfl.ch)the number of ongoing or recently completed research projects in the UK in which precast concrete was the principal feature was about8(of which the author was involved in4).In 14European(including Nordic)countries the average per country was around12.It is estimated that by proportional representation of the research effort,the market share for precast concrete would be around 2}3%!
This paper reviews some of the key elements of research and development on precast skeletal frames, and examines why the research effort serving this highly respected sector of the construction market is so disproportionately low.
2.Categorizing the extent of research activity
Research activity on precast concrete frames can be broadly subdivided as:
E studies on global precast frame behaviour,focusing on the influence of connections;
E substructuring of precast frames into appropriate two-dimensional cruciform or floor bay assemblies for the benefit of convenient experimental testing and/or numerical modelling,such as finite elements;
E optimization and advancement of precast elements, in particular lightweight prestressed floor systems;
E vertical and horizontal stability systems,such as infill shear walls and precast floor diaphragms without cast in situ structural toppings;
E connections and joints;
E structural integrity,a theme word for the collective issues of ductility,toughness and robustness. North American,Central European and Scandinavian academics and industrialists,working in partnership,and publishing in teams,have often dominated research and development work. Concerted programmes have rarely crossed continental boundaries,so that‘reinvention of the wheel’to satisfy national practices is commonplace. Localized pockets of activity are found in countries such as Brazil,Portugal,South Africa,Singapore and New Zealand.Although individual research is well directed and compliant with the profession’s needs, the broader picture is fragmented and,unlike research on structural steelwork,difficult to collate.The main exception to this is the dissemination of research results by the Prestressed/Precast Concrete Institute, 209West Jackson Boulevard,Suite500,Chicago, Illinois,60606,USA(PCI)in the and the FIB.
In the UK,research has followed a pattern of innovation}optimization}change,the cycle being repeated approximately every10}15years,albeit in different subjects.It has been industry driven because of the fact that it is impossible to divorce the fundamental behaviour of precast structures from the ‘design}manufacture}construct’philosophy,an approach which is unique to precast concrete.The research is often seen as being‘near market’.This shifts the academic balance towards the precast manufacturers,much to the displeasure of some funding bodies.Although the precast industry actively supports research,it somehow undervalues research expertise,so that only a handful of research leaders have the appropriate industrial background necessary to carry out the work to the prenormative stage.
3.Studies on global precast concrete frame behaviour
There has been very little research into the behaviour of complete structures,even though the profession generally agrees that such research would enhance the status of precast frames by demonstrating their unquestionable structural integrity.A number of projects have actually been successful in demonstrating precast integrity by placing the emphasis on the continuity of connections rather than on the elements themselves.The most notable of these has been the PRESSS(Precast Seismic Structural Systems)Project[3,4,5],a collaboration in seismic research between academics and professional engineers in Japan and the USA.The objectives of PRESSS,which began in1990,were to develop new materials and structural systems for multi-storey precast systems in seismic zones,leading to calculation models suitable for code drafters to use.In the final stages of the programme,a60%scale, 30;30ft,five-storey(9.15;9.15;11.43m)precast beam and column sway frame,Fig.4,stabilized with shear walls in one direction only,was tested at the University of California,San Diego in1999.
In the direction of the two bay sway frames,one line of beam}column connections was prestressed,whilst the other line was not.In the prestressed line the
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Fig.4PRESSS five-storey sway frame under seismic load test. Reproduced by permission of J Stanton,University of Washington, Seattle,
USA Fig.5Moment d sway deflection in PRESSS frame test[6]. Reproduced by permission of PCI
precast beams for the lower three storeys spanned face-to-face between columns and were post-tensioned to them.For the upper two storeys precast pretensioned beams were used that were continuous through the columns.For the non-prestressed frame line,moment resistance for the lower three storeys was provided by tension/compression yielding(TCY,see later in this section)gap connections.For the upper two storeys the TCY connection was again used and both the top and bottom mild steel was grouted in ducts.
The frame was designed with a‘direct displacement design’procedure,in which inelastic target displacements(as determined by storey height drift factors)and effective(secant)frame stiffness are the design objectives.This approach is opposite to the load-based approach normally used for seismic design,where load capacity and ductility are the design objectives,and deflections,rotations,strains, etc.are measured inter alia.
Priestly et al.[6]report that pseudo-dynamic horizontal loads were applied at floor levels,giving a sway/height ratio of up to4%}about20times greater than the value of0.2%(1in500)accepted in a static frame for elastic response at design loads and about twice the target‘design displacement’for strength-based design seismic forces.This resulted in sway displacements of about450mm at the top storey.The maximum reversible shear at the base reached 1500kN,equivalent to a static horizontal pressure on the facade of the building of approximately
14kN m\2.The total overturning moment acting on the eight18-in(457-mm)square columns ranged from 6000to12000kNm,although actual column moments were less than this because of the flexural frame action. The author has calculated that the sway deflections reported by Priestly are some6times those in an elastic monolithic framework of similar dimensions and cross-section subjected to the same,but static,load pattern.
The moment}sway deflection curves in Fig.5for the structure as a whole show residual sway deflections of less than0.15peak values.The residual sway deflections shown in Fig.5were a result primarily of inelastic response of the non-prestressed frame,and of the connections at the base of the columns for the prestressed frame.Inelastic response,which occurred at load levels of about50%of maximum,was due to cracking near the beam}column connections,as intended.Shear cracking in the column was a feature of the damage,as shown in Fig.6,for the
beam}column joints of the non-prestressed frame at the seismic strength design level drift of about2%.By contrast,shear cracking of the column for the joints of the prestressed frame was minimal at the same drift level.
The conclusions of the results published up to December1999are:
E the test has provided good confirmation of the direct displacement approach used to determine the strength and stiffness of the frame;
E sway deflections of twice the seismic strength-design approach value of2%of the height were achieved without any loss of gravity load-carrying capacity;
E under the dynamic loading,greater forces than expected were sustained in the floor diaphragms, which translated into storey shear forces much greater than the anticipated code values;
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Fig.6Shear cracking in columns in PRESSS frame test[6].Reproduced by permission of PCI
E analytical models have been used to predict the response of the frame with excellent corroboration }no worse than around10%variation on average. The message for designers of precast frames, whether seismically loaded or not,is that it is possible, with attention to detail,to develop ductile precast concrete unbraced frames several storeys high.For seismic design of precast concrete frames in the USA, the current concrete code,ACI318-99,requires that it be demonstrated by experimental evidence and analysis that such frames will have strength and toughness equal to or exceeding that provided by
a comparable monolithic reinforced concrete structure designed in accordance with that code’s requirements for special moment frames.However,for the next code,ACI318-02,provisions similar to those of the 2000NEHRP(National Earthquake Hazards Reduction Program)Recommended Provisions[7]will allow use the use of precast frames in high seismic zones of the types tested in the PRESSS building. Conditions that must be met during validation testing of modules representing such precast frames are specified in a recently published ACI Standard[8].As of December2000there were eight skeletal precast frame structures either built or under construction in high seismic zones in the USA that utilize the post-tensioned frame type of the lower three storeys of the prestressed frame in the PRESSS building.The tallest structure is a44-storey building in San Francisco.
In the wider scheme of PRESSS,connections for precast frames have been tested and classified as:E‘strong’,causing inelastic deformations to occur away from the joints;
E‘ductile’,causing energy dissipation and being more ductile than the frame elements;
E‘extensible’,enabling large deformations at low resistance,such as simply supported beams seated on elastomeric pads.
Fig.7shows examples of ductile beam}column connections.Fig.7(a)shows the connection used for the upper two storeys of the prestressed frame of the PRESSS building.Connections that were refinements of the NIST connection of Fig.7(b)were used for the lower three storeys of the prestressed frame in the same building.Shear capacity at the column face is provided by post-tensioned dowel action of unbonded tendons stressed to0.5f pu and by friction from the continuity reinforcement.By interarticular grouting at the bottom of the beam,continuity bars are able to yield without damaging the concrete during large rotations.Under cyclic deformations the tendons remain elastic.To provide ductility static rebars are added to the top and bottom of the beam,which yield and dissipate energy to dampen the structure.Fibre reinforcement is used in the infill to prevent grout spalling.
Earlier tests[3]were carried out on a variety of scaled models of various connections being considered for the non-prestressed frame of the five-storey PRESSS building.Based on those test results the TCY (tension}compression}yield)connector,shown in Fig.7(c),was selected for use in the building.That connection was demonstrated to enable frame sway C ONCRETE CONSTRUCTION
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Fig.7Beam d column joints used in the PRESSS project:(a)post-tensioned connector [3];(b)‘NIST’connector [5];(c)TCY connector [3].Reproduced with permission
deflections up to 2%of the height [3]without loss of gravity load-carrying capacity.Even at a sway deflection of 0.2%of the height,the horizontal load pressure equates to about 3.5kN m \2,some 3times greater than normal static ultimate wind pressure.
Further frame studies in Japan have focused on the role of the beam }column interface on frame stiffness [9,10].Joints assembled with continuity
reinforcement and steel plates were tested in a large
cruciform arrangement at full scale,500mm deep ;400mm wide beams.Fig.8shows the load Q }deflection response of one of the more heavily reinforced specimens.If the normal serviceability loading on such a frame is considered,the
displacements are well within the linear elastic range.In Scandinavia,a number of ‘new’framing systems have been researched.The shallow slab }beam }column arrangement shown in Fig.9uses low-level steel corbels to support long-span beams and floors [11].
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Fig.7(continued
)
Fig.8Load d displacement curves in seismic precast frame tests [9].Reproduced by permission of Routledge
A main feature of this system is the remarkable
span }beam depth ratio of around 20:1to 25:1achieved for office loading (5kN m \2).Suikka [12]reviews several proprietary prestressed and reinforced concrete floor systems,including the ‘slim floor’
system,in which the concrete flanged beam in Fig.9is replaced with a steel plate beam for spans up to 9m.Although the papers by Pessiki et al .[13,14]do not provide new research data,19precast structural floor systems for office buildings are reviewed and
assessed.Noting that the structural layout has a major influence on overall building height,and services and communication routes,a call is made to architects for the services to be installed within the structural
elements.Elements that require horizontal services to be threaded through openings reduce service route options and often limit the physical size of the installations.Surprisingly,most systems have
maximum spans of around 9m,and limited spatial (three-dimensional)versatility.
Summarizing comments:
Research on the behaviour of complete skeletal structures has satisfied the need to demonstrate ductile behaviour under large cyclical horizontal displacements.Where ductile connections are provided at beam }column joints,sway
deflections of up to 1/25of the height of the structure have been achieved.The response remains elastic even where the horizontal load is in excess of typical ultimate wind pressures.Attempts to provide precast concrete with an alternative design for flat slab construction has led to the development of shallow-flanged
concrete and structural steel beams.When used with prestressed hollow core units floor bay areas of around 70}80m 2are possible,less than 350mm deep.
4.Advancement and optimization of precast elements
Precast concrete frames consist of two types of elements:
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Fig.9Shallow-beam construction methods[11].Reproduced by permission of Addtek R&D
E‘sturdy’elements such as columns and walls,where technical advancement has been slow in recent years; E‘slender’elements,such as long span shallow beams and voided floor slabs,where considerable research has been devoted to their optimization, manufacture and design.
Researchers have attempted to keep pace with the increased sophistication with which elements such as prestressed hollow core units(hcu)for floors are being designed and manufactured.As European production of hcus is currently around25;106m2per annum,and profit margins hover around5%,commercial advantage is being sought through technological advancement.
Hollow core units were developed in the1950s when long-line prestressing techniques evolved alongside horizontal extrusion or slip-forming concrete production methods.For30years the units changed very little,although some advances were made in improving the cross-section profile.The1980s then saw an upsurge in research and development, aimed at gaining a greater understanding of the behaviour of these units.This activity has continued to the present day,thanks to the efforts of manufacturers and organizations such as IPHA(International Precast Hollow-core Association c/o Mr A Crane,The Ramblers,Bank Road Penn,High Wycombe,Bucks, HP108LA,UK)and the UK Precast Flooring Federation(60Charles Street,Leicester,LE11FB, UK).
Research work has been carried out in the following areas:
E improving the reliability of calculation models for the flexural,shear,torsion and bearing strengths, and the flexural stiffness of prestressed units;
E transmission lengths and lateral bursting stresses in the transmission zone of prestressed units;
E reduced shear capacity of hcus bearing onto flexible beams;
E lateral load distribution for point and line loads in hcu slab fields;
E continuity of bending moments in hcus at interior supports;
E shear friction in the longitudinal joints between hcus;
E horizontal floor diaphragm action without structural toppings;
E behaviour in fire.
4.1S HEAR AND BOND STRENGTH OF PRESTRESSED HOLLOW CORED UNITS
Flexure is a predictable mode of action in these units. The cracking and ultimate moments of resistance can be calculated with accuracy.FIP,PCI and other documents[15}17]provide calculation models for bending and shear resistance,but it is the latter where most research has been carried out.
Girhammer[18],Pisanty[19],Olsen et al.[20]and Lin Yang[21]have carried out extensive studies on the shear capacity of prestressed hcus.Pisanty made
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Fig.10Finite element modelling of transmission zone in hollow core units[23].Reproduced by permission of M.Akesson
worrying comparisons with the BS8110code equation for ultimate shear capacity V co by suggesting that
a10%reduction in the calculated value of V co was necessary to give close agreement(&1.05)with test values.Lin Yang questioned the appropriate distance from the end of the unit at which shear capacity should be calculated.He suggested that it should be at the neutral axis,on a line drawn from the front edge of the bearing and inclined at353(not453).That line intersects the neutral axis further from the end of the unit than is the https://www.doczj.com/doc/7a8804642.html,parisons with118tests carried out at VTT in Finland obtained95%agreement with this hypothesis.The key to this matter hinges on the length l t of the transmission zone governing the build-up of prestress at the neutral axis.
Walraven&Mercx[22]have reported that the ACI 318Commentary equation for l t"f pe /21is adequate, where f pe is the effective stress in the tendon and is the diameter of the https://www.doczj.com/doc/7a8804642.html,ing finite element models(Figure10)Akesson[23]found that the denominator in this equation should be about38,and that strand pull-in was less than one-half the normally accepted value of1.5mm.In the USA it is known that,dependent on the surface condition of the tendon, transfer lengths can vary between one-half and twice the values given by the equation in the Commentary to the Code,and for that reason the equation does not appear in the Code.Rapid transfer of stress led to large lateral splitting stresses sp of around2.2N mm\2in Akesson’s models.Den Uijl[24]provided data enabling designers to check sp,as shown in Fig.11[15].Fig.12is proof that splitting stresses and pull-in are related.
4.2S HEAR REDUCTION OF HCU ON FLEXIBLE SUPPORTS
Traditionally,shear tests had always been carried out on rigid supports.In this manner the shear stress in the web is two-dimensional,i.e. zy,as shown in Fig.13(a).However,if the units are seated on flexible supports(Fig.13b),the curvature of the beam causes lateral curvature of the floor unit,resulting in transverse shear stress zx.Pajari[25]carried out full-scale tests,comprising double spans of
7.2m;265mm deep hcus,five abreast,supported on
a range of precast inverted T-and steel-plate beams in C ONCRETE CONSTRUCTION
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Fig.11Graph to determine splitting stresses due to prestress [24].Reproduced by permission of Fe de ration International du Be ton
such a manner that both the slabs and beams
were in bending.The startling result was that the shear web capacity of the hcus on flexible supports was 23}60%lower than in a reference test on a rigid support.
Pajari proposed a calculation for strength,involving the principal stress vector in a three-dimensional stress field as follows [25].The critical element in the web is subjected to:
E f cp due to the effective prestressing force "f pe A ps /A c ;E zy due to the vertical shear force V where
"VS /Ib v is calculated at the neutral axis;E zx due to the shear flow in the transverse direction,which is a function of the flexibility of the
supporting beam and the ratio of the breadth of the webs to the breadth of the hcu.In this state of stress,according to BS 8110,the principal tensile stress "
f cp 2
f 2cp 4
# 2zy # 2
zx (f t "0.24(f cu (1)
in EC 20.24(f cu is replaced by f ctm .Theoretically zx "
3vb 4b v h ct
(2)
where b "breath of unit,usually 1.2m;b v "total breath of web per hcu;h ct "critical web depth,
defined in Fig.13(c);and v is the transverse shear flow due to maximum imposed shear force in the beam V b ,given as:v "
y t EA f V b
EI
(3)
where y t "centroidal distance to the top of the slab from the neutral axis;EA f "axial stiffness of top flange of slab "b eff h f ;EI "flexural stiffness of the composite beam;and h f "thickness of top flange of hcu.
Referring to Fig.13(d),the effective breadth b eff for the total compressive flange width (i.e.on both sides of the beam)is found experimentally because of the complex interactions between the hcu,infill concrete,interface shear reinforcement and beam.For a typical precast concrete inverted T-beam (the most common type)b eff +400mm.Other values are given by Pajari [25].
This calculation enables a comparison to be made between the shear capacity of a unit where zx is zero and where it is finite.Designers responded to these findings by pointing out that the shear capacity of hcus is rarely critical,and even a 50%reduction in strength
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Fig.12Splitting cracks due to excess prestress and strand
pull-in
Fig.13Reduced shear capacity of hollow core floor units on flexible supports [25];(a)web shear stresses;(b)result of flexible supports;(c)definition of h cr ;(d)definition of b eff .Reproduced by permission of ASCE
would rarely cause embarrassment to the design of existing hcus on flexible supports.However,this issue may well be of significance for hcus in high-risk
seismic zones where there may be a significant vertical component to the earthquake motion.
4.3L ATERAL LOAD DISTRIBUTION FOR POINT AND
LINE LOADS IN HCU SLAB FIELDS
Voided floor slabs,such as hcus,do not contain web reinforcement,but are expected to resist torsion and transverse shear (due to the development of
precompression,according to eq.1)in order to act in an orthogonal manner and enable lateral load transfer.Their capacity to do so in a ductile manner was investigated by Clark &Thorogood [26]who tested 300-mm-deep voided slabs with and without shear links in the webs.The average failure load in the units without shear links was 0.6times those with shear links.Seven of ten specimens failed by horizontal web splitting due to transverse Virendeel action of the webs and flanges.In spite of these results designers accept transverse shear by permitting load sharing between adjacent units,relying on the shear key to transmit loads across the longitudinal joints and on the torsional strength of torsionally unreinforced units.Point loads and line loads parallel with the direction of span give rise to bending moments in a direction at right angles to the direction of span,and to vertical shear forces in the longitudinal joints between adjacent units.The joints between adjacent units behave as hinges,capable of finite moment and full shear
transfer.These loads produce shear in the longitudinal edge of the adjacent units.This shear induces torsion,which is limited by the tensile capacity of the concrete.The deflected profile of the total floor slab is computed using finite strips and/or differential analysis.In this way the load carried by each unit distanced progressively further way from the load is
determined.Results are presented graphically,as shown in Fig.14[12]for 1200-mm-wide units.Fig.14shows,for example,that for a span of 8m the unit on
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Fig.14Line load distribution coefficients for 1.2-m-wide hollow core units [15].Reproduced by permission of Fe de ration International du Be
ton
Fig.15Continuity reinforcement in opened cores of hollow core floor units at internal supports
which a line load is erected carries only 30%of that load,whist the adjacent units carry 20%each,and so on.If the said unit is located at an unsupported edge,the proportion of these loads increase to 51and 31%,respectively.Similar data exist for point loads [12].
Stanton [27]determined distribution widths resulting from point loads,not only near the centre of the floor area,but also close to free longitudinal edges.Results suggest that if a point load is acting at mid-span over a length L ,then the distribution width is 0.35L either side of the centre of the loaded unit.If the point load is at one-quarter span,the distribution width is 0.28L
either side.Applying these results to spans of 6}8m,the loads are being distributed over five units of 1.2m width.These results are in good agreement with the values in Fig.14.
4.4C ONTINUITY OF BENDING MOMENTS AT
INTERIOR SUPPORTS
In the past 20years practical experience has been gathered in making the simply supported ends of hcus flexurally continuous at interior supports,both with and without structural toppings.This is common in seismic countries where the action is used more for structural integrity than for increased moment capacity.However,the negative restraint moment capacity must be considered at both the serviceability and ultimate limiting states.Fig.15shows a typical detail }site-placed reinforcement of maximum
diameter 6#h /25(h "depth of hcu in mm)is cast in situ (grade C40concrete minimum)into top-opened cores,overlapping (not physically touching)with factory-placed upper prestressing tendons.At least three cores in a 1.2-m-wide unit (four if the span is greater than 6m )should be filled.Design procedures,based on full-scale testing (e.g.Levi &De Barnardi [28]and Grzybowski &Westerberg [29]),are now published [30].
The main points are:E the length the site bars must penetrate into the opened cores is at least two bond lengths,but not less than the transmission length of the upper tendons;
E the negative moment of resistance is relevant only to the imposed loads,and is provided by an
appropriate area of reinforcement calculated in the normal manner.Crack widths are calculated at the service load;
E to cater for the long-term effects of relaxation,
shortening of the hcu,creep,shrinkage,etc.induced rotations at the ends of the hcus cause positive
P RECAST CONCRETE FRAMED STRUCTURES 417
Fig.16Perimeter reinforcement and coupling bars in precast floor
diaphragm
Fig.17Shear failure in precast hollow core floor diaphragm tests (courtesy K Bensalem,University of Nottingham,UK)
sagging moments,which in some cases (long span,sustained loads)may be greater in magnitude than the negative moment;
E the shear capacity of the section is based on the non-prestressed section;
E continuity leads to an increase in the span to depth ratio,typically from 30}35,with a small reduction (about 5%)in the required area of prestressing tendons;
E the net increase in cost in achieving continuity,including the extra work at the factory in making the slots,is less than 5%.
4.5H ORIZONTAL DIAPHRAGM ACTION IN HOLLOW
CORE FLOORS WITHOUT STRUCTURAL TOPPINGS
There was considerable debate in the profession some 25years ago whether or not a horizontal floor
diaphragm could be provided solely using discrete precast floor units,such as hcus,without the need for a structural cast in situ topping.The evidence today is that,providing the units are adequately tied to prevent their moving apart,the units alone are capable of providing a diaphragm in all situations,except
perhaps seismic situations.To achieve integral action a horizontal shear mechanism resulting from shear wedging,shear friction and dowel action must be generated in the longitudinal joints by the correct placement of site bars and cast in situ concrete infill (grade C25minimum)as shown in Fig.16.The possible seismic exception is because wave action passing through the diaphragm with vertical
amplitude may cause cracking in the longitudinal joints,thus preventing shear wedging and shear friction.
Research into static systems was first carried out on full-scale hollow core slab fields by Sarja [31]and
Svensson et al .[32].These slabs were loaded horizontally in bending and shear,so that the shear mechanism was the sum of flexural and arching actions.These tests,often 20}30m 2in floor area,were too expensive to
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418
Fig.18Shear force d longitudinal slip in joint between adjacent hollow core units [36].Reproduced by permission of The Institute of Structural
Engineers
Fig.19Relationship between shear failure and edge roughness in joint between adjacent hollow core units [37].Reproduced by permission of Routledge
Table 1Initial crack widths between precast units
Age of precast unit Width of longitudinal when joint is filled (days)Width of precast unit (mm)joint (mm)Initial crack width ti (mm)...............................................................................................................................................(7
1200250.2151200500.230600250.115600500.13028
1200250.1351200500.150600250.075600
50
0.090
'90
1200250.0951200500.110600250.055600500.070
...............................................................................................................................................
study the wide range of parameters,such as depth of floor,tie steel density,surface roughness,etc.on which the shear in the longitudinal joint between adjacent units relies.Tests carried out by Moustafa [33],
Stroband [34],Menegotto [35],Elliott et al .[36,37]lead to greater confidence in the use of precast diaphragms.Menegotto developed a novel sinusoidal edge profile (50mm pitch ;6mm amplitude)which enabled
inclined compressive strut action,rather than shear wedging,to develop across the joint.
In the UK the tests carried out (Fig.17)on 200-mm-deep proprietary hcus [36,37]found that the ultimate horizontal shear stress in the longitudinal joint exceeded the BS 8110ultimate code value of
0.23N mm \2by around 30%for pure shear,and by more than 60%for shear and diagonal compression.Fig.18shows the result of reversible load acting on a 4-m-long joint:200kN equates to a net shear stress of about 0.3N mm \2.Clamping forces normal to the precast units resulted in coefficients for shear friction of at least 5,far greater than the value of 0.7normally assumed for concrete-to-concrete friction.Coupling bars,cast in situ into the open-ended cores,eventually succumb to splitting failure,as shown in Fig.17.The longitudinal displacement causes a lateral
displacement,or crack widening,which must be resisted by transverse reinforcing bars placed in the
in situ edge beam,as shown in Fig.16.Experiments have found that these bars must carry tensile forces of
between 40and 75kN at each end of the floor span.This force is approximately the same as the tie force required in stability floor ties according to BS 8110or EC2.
Because the behaviour of the interface depends on the roughness of the sides of the precast units,physical measurements have been made on factory-produced units [37].The roughness factor is represented by R a ,the arithmetic mean deviation of the edge profile (in mm).Values for R a in typical hollow core production are between 0.2and 0.3mm.The results of shear tests made on units with varying degrees of roughness are shown in Fig.19.Even for a smooth surface with R a equal to zero,the extrapolated shear stress in Fig.19is 0.22N mm \2,i.e.just less than the BS 8110design value of 0.23N mm \2.
Cholewicki &Elliott [38]present a calculation model for the strength and shear stiffness of the longitudinal joint based on previous experimental [36]and
P RECAST CONCRETE FRAMED STRUCTURES 419
Fig.20Shear displacements in the total floor diaphragm [38].Reproduced by permission of Bauverlag GmbH
theoretical work [39].Where bending and shear
combine,the shear stress in the longitudinal joint is given as:V !( F c
A
( u
(4)
where V "ultimate horizontal shear force between neighbouring hcus;A "net contact area between hcus,taken as B ;(D !30)mm;B,D "length and depth of hcu; "friction factor,taken as 0.7for concrete-to-concrete friction;F c "compressive force due to diaphragm bending "M h /0.8B ;and M h "horizontal diaphragm bending moment.To maintain shear friction diaphragm
reinforcement,A h is positioned in the chord elements over the tops of the beams at the ends of the floor units,and is determined as:A h "M h 0.8B ;0.95f y #
V
0.6 ;0.95f y
(5)
The shear stiffness of individual joints K s "V / s ,(curve gradient in Fig.18),is used to determine the shear modulus of the diaphragm.A limiting value for the shear displacement s when the joint fails in shear is therefore required.This value is found by limiting the transverse displacement t,max to around half of the maximum value of 1mm found in tests [36,37].According to test results [36]: s,max "
log e ( t,max / ti )
3.0
(6)
The initial crack width ti varies according to
conditions of age,unit width,and longitudinal joint width and is given in Table 1.The shear stiffness of the joint subjected to the greatest shear force gives the defining maximum stiffness of the diaphragm K s,max as:K s,max "V max / s,max
(7)
In the tests,the mean value of K s,max after several reversals of load was about 230kN mm \1per m run (Table 2in Elliott et al .[36]).The maximum applied shear force V should not be greater than
V max calculated from eqs (6and 7),together with this value.As an example,consider a 6-m-long ;200-mm-deep ;50-mm-wide longitudinal joint infilled after
7days:from Table 1 ti "0.23mm,then eq.(6)gives s,max "(log e 0.5/0.23)/3.0"0.26mm,and eq.(7)gives V max "230;0.26"60kN per m
run ;6m "360kN.The interface shear stress,(eq.4), "360;103/6000;(200!30)"0.35N mm \2'0.23N mm \2.The joint is therefore limited by strength and not displacement.
The horizontal deflection of the entire diaphragm is determined by the addition of the shear displacements si (calculated from eq.6)in each longitudinal joint,as shown in Fig.20.The shear displacement in the
precast unit is negligible.This effect can be taken into account by calculating an effective shear modulus G for the diaphragm as:G " "K s,max w B (D !30)
in N mm
(8)
where w "width of the hcu.
The degradation in shear stiffness with increasing load cycles is evident from Fig.18[36].Taking an
average value of 230kN mm \1per m length of contact for all tests,G equates to 1.67kN mm \2.
From the numerous testing programmes carried out on precast floor diaphragms,the results confirm,without exception,adequate interface shear
performance and diaphragm action using normal construction practice.
4.6B EHAVIOUR OF HOLLOW CORED UNITS IN FIRE
For many years,the fire resistance of prestressed hcus was based on cover distance to the strands,with some account taken of the cover distance to the hollow core.Units manufactured from siliceous
aggregates were down-rated against those made from limestone aggregates.Overall,the technology was not advanced in spite of more than 100fire tests
carried out on prestressed hcus since 1970.However,recent fire tests on these units in some laboratories resulted in premature shear failures,although similar failures have never been reported in real
fires.The reason for the shear failures may have been faulty testing arrangements,and/or neglecting the influence of the end connections and the surrounding structure.
Hollow core units have a special cross-section in terms of thermal transmission.The temperature gradient has a strong curvature profile,as shown in Fig.21.Although the deformation is linear through the thickness of the unit,the stress distribution is
nonlinear,resulting in large compressive stresses in the flanges,but tensile stresses in the web.
Calculations show that the tensile stress in the web could exceed the tensile capacity of the concrete after 20}30min in a standard fire test.
In response to this Van Acker [40]reports on four fire tests carried out in Belgium on slab fields,comprising up to eight 3-m-long ;265-mm-deep hcus arranged in a double span,four abreast.The units were connected
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420
Fig.21Strain profiles through hollow core units due to fire acting on soffits [40].Reproduced by permission of Concrete Association of Finland
to perimeter and internal support beams using
between one and four 12-mm-diameter bars.Two of the spans received a cast in situ structural topping.Bending failure occurred in seven out of eight cases (the odd one being a shear failure)at load magnitudes greater than the serviceability live load by factors of 1.78}3.24,the average load factor being 2.72.The explanation of these results is that the omission of shear reinforcement in the web is completely
compensated by the interaction between the units with the surrounding structure.This prevents fire-induced cracks from initiating shear cracks,enabling aggregate interlocking such that the shear capacity is not affected by fire.The research continues.
Summarizing comments
Hollow core units are sophisticated prestressed concrete elements used in floors with large
span-depth ratios,typically 30}40.Although the units are designed and manufactured as simply supported one-way spanning,their behaviour in a three-dimensional slab field leads to complex stress patterns,owing to interactions between neighbouring units,supports,and cast in situ topping,etc.As a consequence of this action,manufacturers have sponsored wide-ranging research to develop or enhance the reliability of published calculation models.Full-scale testing has been successfully applied to mitigate the profession’s fears on matters such as fire,reduced shear on flexible supports,splitting stresses in transmission zones,and floor diaphragm action.
5.Studies on precast frame connections
Frame action in bending is rarely considered by designers of precast frames,in the belief that
connections made by site welding,grouting or bolting are insufficiently ductile,or have low rotational
stiffness at low loads.The work of Cranston [41]led to the present UK design rule that the effective length factor of a column in a pinned-jointed precast skeletal frame should be taken as 2.3over the full height of the column.This requirement is because the ratio of the
flexural stiffness of a precast beam to that of a precast column was estimated to be about 1/10.This
estimation,however,ignores moment continuity from the column to the beam,or vice versa,even if it is accompanied by beam rotation.
Fig.2shows that if the rotational stiffness of
a beam }column connection is greater than about 0.4times the flexural stiffness of the beam (4EI /L )the sway stiffness of a structure containing that joint is about 95%of an equivalent monolithic frame,i.e.the ratio of the sway deflection in a frame containing this flexible joint is only 1.05times the sway in an identical monolithic frame.This idea dates back to the 1930s when semi-rigid connections were first conceived.Now,more than 60years later,the move towards semi-rigid connection design in structural steelwork has awakened the precast concrete industry to the need to study the same issue.
5.1R ESEARCH PROGRAMMES ON STRUCTURAL
CONNECTIONS
From 1989to 1998projects on semi-rigid precast connections were carried out simultaneously in the UK,Finland,France,USA,Brazil,etc.In Europe the COST C1Action [2]was established to control the behaviour and design of semi-rigid connections in a range of materials:precast concrete,structural steelwork,steel }concrete composites,timber and polymeric composites.Some 25countries and more than 125research centres were involved.Not
surprisingly the results were as diverse as the wide range of materials and geometry studied.The original aims of being able to ‘classify’all connections as either flexible,semi-rigid or rigid,depending on their
influence on the buckling resistance and sway stiffness of frames,could not be agreed on,as the complexity of the task increased under the weight of the research effort.Essentially,the power of computers to analyse structures containing material and geometric nonlinearity usurped the need for classification
boundaries,which were found to differ according to material type,stress history and loading regime.If COST C1achieved anything it declassified the constitutive boundaries previously laid down for semi-rigid connections.
P RECAST CONCRETE FRAMED STRUCTURES 421
Fig.22Construction of precast beam d column connector (courtesy H Gorgun,University of Nottingham,
UK)
Fig.23Definition of moment-relative rotation and beam line
Precast concrete connections (Fig.22)were found to be influenced by many effects,and particularly those connections involving an assembly of welded plates,grouted dowels or bolted brackets }the vast majority of connection types.Semi-rigid behaviour is described by a moment-vs.beam }column rotation (M } )diagram,idealized in Fig.23.There is a zone of
influence beyond the immediate locality of the joint,approximately equal to the cross-sectional dimensions of the adjoining beam and column members.In this context,it is very important that the characteristics of the connection are tailored to suit the requirements of the adjoining members.The beam-line method,
illustrated in Fig.23,is therefore used to quantify this relationship.
The work on the stability behaviour of reinforced concrete beam }columns by Cranston [41]was extended by Virdi &Ragupathy [42]to include the M }
characteristics of connections.An iterative computer program,known as SWANSA (sway and no sway analysis)was developed to take account of the real behaviour of semi-rigid connections.The iterative numerical procedure is based on the calculation of the equilibrium-deflected shape of the frame.At a given load factor,when an equilibrium-deflected shape cannot be found,this load is the ultimate load capacity of the whole frame.The program was validated against the results of eight full-scale axial load tests,each comprising one column containing a single precast beam connection [43].Because of this
arrangement,the tests were unable to provide data on reciprocating frame action following curvature of the column.This limitation has been a feature of most of the tests carried out on isolated connections.
SWANSA has been used to show the differences in using pinned,semi-rigid,and rigid connections in multi-storey frames [44].Fig.24shows output bending moment distributions of a three-storey frame
subjected to floor gravity loads.The maximum beam UDL attained in the pinned,semi-rigid and rigid
jointed frames was 64,108and 127kN m \1,
respectively.When the same frame was subjected to horizontal sway loading,the maximum horizontal load s per floor in the same three cases were 5,24and 30kN,respectively.Thus,the failure loads in the semi-rigid frame were about 0.8times of those in the fully rigid frame,and up to 4.8times greater than those in the pinned-jointed frame.
The conclusion is that semi-rigid connections act more like rigid connections than pinned.The problem now was to demonstrate that typical precast
connections could develop sufficient stiffness and strength to foster frame action in this manner.The two methods of collecting the necessary data were full-scale experimental testing and finite element analyses.
5.2M OMENT `ROTATION TESTS ON BEAM `COLUMN
CONNECTIONS
The preferred method of making beam }column
connections in skeletal frames is to attach the end of the beam to the column face via a concrete corbel,steel billet (Fig.22)or stiffened steel angle.At this stage of construction the joint is most definitely pinned.But
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Fig.24Bending moments in pinned (left)and semi-rigid (right)sway frames
[44]
Fig.25Shear cracking due to flexure in beam d column connection tests [45]
when precast floor slabs and tie bars are included the connection possesses flexural strength and stiffness to resist imposed gravity and wind loads.Although this action may be limited in a sagging bending mode,where the bottom of the connection is in tension,it is of considerable magnitude in a hogging mode,where tie steel in the floor may be designed to yield.
Twenty-three experimental tests gave real semi-rigid M } data for a wide range of connections [43,45}48].Fig.25shows damage to columns following reversible static sway loading }note the similarity to the column in the PRESSS frame in (Fig.6).Fig.26shows M } plots for single-side moments (edge column situation)and balanced moments (interior column).The
intersection of these plots with the beam lines (Fig.23)gives a design point E where the end rotation of the beam and that of the connection are equal.The secant gradient is called J E .At the ultimate limit state,the
maximum strength of the connection should be greater than M E .The final rotation of the connection should be greater than the rotational capacity of the beam u .Results varied enormously,e.g.strengths from 18to 238kN m,and secant stiffnesses J E from 900to
44000kN m rad \1.(Not all connections were suitably semi-rigid,and those must be designed as pinned joints.)However,as shown in Fig.27,by dividing the strength of the connection by that of the beam,
M U /M R ,and letting K s equal J E L /4EI ,the following empirical equations are approximated from the data points:
M U
M R
"0.87(K s for the single-sided tests (9)
M U
M R
"0.62(K s for the double-sided tests (10)
P RECAST CONCRETE FRAMED STRUCTURES 423
Fig.26Moment d rotation curves for double-sided and single-sided beam d column connection tests[43,44]:W"welded steel narrow plate
connector;B"steel billet connector;PSF"with partial safety factors applied to loads and
materials
Fig.27Relationship between connection moment and stiffness[44] The increase in stiffness for the double-sided tests is a consequence of the available continuity through the column,which cannot take place in single-sided connections.This is particularly noticeable under balanced gravity loading,where the strength and stiffness of the column do not influence connection behaviour.
Therefore,as M U and M R may be readily calculated, the stiffness J E of the connection may be determined from eqs.(9,10).Furthermore,the relation between M E and M R may be deduced from the beam-line as:
M E M R "
J E
(J E#2EI/L)
(11)
Designers should not be afraid of specifying semi-rigid connections because their construction is exactly the same as a pinned joint,so long as continuity is provided,usually in the form of stability tie steel,and the usual quality control procedures are recognized. Researchers believe that if the results from these tests, combined with the further finite element simulations carried out on similar connections[49],are used in frame analysis programs(such as SWANSA), designers have no grounds for objection.If designers do not wish to resort to computer programs,the column effective length factors described in the next section may be considered.
5.3C OLUMN EFFECTIVE LENGTH FACTORS IN
SEMI-RIGID FRAMES
A linear elastic,geometric second-order two-dimensional computer program was used to determine effective length factors( factor)for columns in various types of sway frames[46].These values may be used to determine the second order moments M add,which,when added to frame moments, should not exceed M E given by eq.(11).A fuller explanation of this procedure is given in a frame example by Elliott et al.[46].
Fig.28(a)shows one of the sub-frames studied.This sub-frame is presently not catered for in codes of practice,and represents a situation where the bottom of one of the columns is fixed rigidly adjacent to the top of a shear wall at the floor below.(Ground and upper floor sub-frames are also given by Elliott
et al.[46]).Fig.28(b)shows the variation in with K s and ,the stiffness of the column relative to that of the beam.It is found that for values of K s(2the factors are more sensitive to changes in K s than .This is an important result because experiments have found K s to be less than2.5.The equations are:
"1#1
1.25#
2.5K s#2.5K2s
#
2.25#0.5K s
for0.1(K s(2(12) C ONCRETE CONSTRUCTION
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