Fib hollow core floors 9x (Last Draft)

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Task Group DRAFT 
 
 
 
Task Group DRAFT 
Acknowledgements 
 
This guide to good practice was drafted by Task Group 6.1, Precast Prestressed Hollowcore 
Floors, in Commission 6, Prefabrication. 
 
Authors 
 
 
Additional contributors 
 
 
 
 
In memoriam Arnold Van Acker 
Task Group DRAFT 
Foreword 
 
 
Prestressed hollow core slabs are amongst the most widely used and investigated precast 
elements for floors and roofs. They offer considerable scope for new uses in the demands in 
the domain of future building construction: structural efficiency, long spans up to more than 
20 m in combination with shallower construction depths, reduced use of materials, energy 
and waste at production, semi-automatic manufacture, etc. 
In 1988 the FIP Commission on Prefabrication published design recommendations for ‘Precast 
prestressed hollow core floors’. The document has been widely used by designers and served 
as a basis for national and international standards on the matter. 
In 1988 complementary guidelines for the design were published as FIP/fib guide to good 
practice ‘Composite floor structures’ and in 2006 as fib Bulletin 6 (Guide to good practice) 
“Special design considerations for precast prestressed hollow core floors” [15]. 
Since this publication, the prestressed hollow core slab itself, the use of the HC slab, the 
functions of the HC floor and the knowledge on the performances of prestressed hollow core 
floors in various applications have evolved a great deal, which justifies a complete revision of 
the design recommendations. 
The present document is intended to complement existing recommendations. It comprises 
two parts: Part 1 with theoretical rules and guidelines, Part 2 with worked calculation 
examples. 
 
Stef Maas 
Chair of fib Commission 6, Prefabrication 
 
Task Group DRAFT 
Contents 
 
1 Introduction ....................................................................................................................................... 1 
2 General information ......................................................................................................................... 3 
2.1 Product description .................................................................................................................. 3 
2.1.1 Cross-sections ................................................................................................................... 3 
2.1.2 Fitting slabs ......................................................................................................................... 4 
2.1.3 Geometrical flexibility ...................................................................................................... 5 
2.2 Methods of manufacture ......................................................................................................... 5 
2.3 Design methodology................................................................................................................. 8 
2.3.1 Procedure ........................................................................................................................... 8 
2.3.2 Design parameters ............................................................................................................ 9 
3 Design of the cross-section .......................................................................................................... 10 
3.1 General ...................................................................................................................................... 10 
3.2 Minimum thickness of webs and flanges ............................................................................ 10 
3.3 Basic design principle .............................................................................................................. 11 
3.4 Prestressing .............................................................................................................................. 12 
3.4.1 Transfer of prestressing ................................................................................................ 12 
3.4.2 Stresses in the transmission zone ............................................................................... 13 
3.5 Checks in Ultimate Limite State .......................................................................................... 15 
3.5.1 Flexural capacity .............................................................................................................. 15 
3.5.2 Anchorage ........................................................................................................................ 16 
3.5.3 Shear capacity .................................................................................................................. 18 
3.5.4 Shear-bending interaction ............................................................................................. 24 
3.5.5 Shear capacity of elements subjected to torsion ..................................................... 25 
3.5.6 Shear and torsion interaction ...................................................................................... 30 
3.5.7 Cracking due to torsion ................................................................................................ 36 
3.5.8 Other design considerations ........................................................................................ 39 
3.6 Minimum reinforcing areas ................................................................................................... 40 
4 Design of hollow core floors ....................................................................................................... 42 
4.1 General ...................................................................................................................................... 42 
4.2 Structural integrity .................................................................................................................. 42 
4.2.1 Tie systems ....................................................................................................................... 42 
4.2.2 Types of floor ties and resistance ............................................................................... 42 
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4.3 Camber design and deflection .............................................................................................. 45 
4.3.1 Introduction ..................................................................................................................... 45 
4.3.2 General aspects ............................................................................................................... 45 
4.3.3 Correction of differential camber between adjacent slab units ........................... 48 
4.3.4 Active deflection of a hollow core floor ................................................................... 48 
4.3.5 Simplified method for the evaluation of camber and possible deviations .......... 49 
4.4 In-plane actions ........................................................................................................................ 52 
4.4.1 General.............................................................................................................................. 52 
4.4.2 Transmission of external forces to the diaphragm ................................................. 53 
4.4.3 Diaphragm strength ........................................................................................................ 55 
4.4.4 Floors with structural topping ..................................................................................... 59 
4.4.5 Floors without structural topping ............................................................................... 60 
4.4.6 Connections to bracing units ....................................................................................... 62 
4.5 Transversal load distribution ................................................................................................63 
4.5.1 General.............................................................................................................................. 63 
4.5.2 Load effect mechanism .................................................................................................. 63 
4.5.3 Design approach ............................................................................................................. 64 
4.5.4 General assumptions ...................................................................................................... 67 
4.5.5 Calculation method ........................................................................................................ 68 
4.5.6 Load distribution factors ............................................................................................... 69 
4.6 Structural toppings and composite action ......................................................................... 75 
4.6.1 General.............................................................................................................................. 75 
4.6.2 Interface characteristics and composite action ........................................................ 76 
4.6.3 Calculation of the interface shear capacity ............................................................... 77 
4.7 Restrained composite supports ........................................................................................... 78 
4.7.1 Introduction ..................................................................................................................... 78 
4.8 Non-rigid supports ................................................................................................................. 80 
4.8.1 General.............................................................................................................................. 80 
4.8.2 Structural behavior ......................................................................................................... 80 
4.8.3 Hollow core floors with longitudinal continuity ...................................................... 82 
4.8.4 Free supported hollow core units on non-rigid supports ..................................... 82 
4.9 Design of cantilevered slabs.................................................................................................. 91 
4.10 Unintended support restrainment ...................................................................................... 91 
4.11 Hollow core floors subjected to horizontal actions ....................................................... 96 
4.11.1 Buckling in the longitudinal direction ......................................................................... 97 
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4.11.2 Behavior of the floor slab in the transverse direction under horizontal soil 
pressure ............................................................................................................................ 98 
4.12 Dynamic actions and vibrations ........................................................................................... 98 
4.12.1 Introduction ..................................................................................................................... 98 
4.12.2 Vibration acceleration .................................................................................................... 99 
4.12.3 Natural frequency ......................................................................................................... 100 
4.12.4 Rhythmic vibrations ...................................................................................................... 102 
4.12.5 Span versus frequency data ........................................................................................ 103 
4.13 Fire resistance ........................................................................................................................ 106 
4.13.1 Mechanical Resistance .................................................................................................. 107 
4.13.2 Integrity of the floor for separating function .......................................................... 120 
4.13.3 Insulation of the floor .................................................................................................. 120 
4.14 Connections ........................................................................................................................... 122 
4.14.1 General............................................................................................................................ 122 
4.14.2 Connections at supports ............................................................................................. 122 
4.14.3 Longitudinal joints between hollow core units ...................................................... 131 
4.14.4 Connections at lateral joints ...................................................................................... 132 
4.14.5 Recommended detailing .............................................................................................. 134 
4.15 Fasteners for moderate loads ............................................................................................ 142 
4.16 Openings and cut-outs ......................................................................................................... 144 
4.16.1 General............................................................................................................................ 144 
4.16.2 Design of openings ....................................................................................................... 145 
5 Hollow core floors in seismic regions ..................................................................................... 153 
5.1 Introduction ........................................................................................................................... 153 
5.2 General aspects ..................................................................................................................... 153 
5.3 Diaphragm action of hollow core floors subjected to seismic actions ..................... 153 
5.3.1 Floors with a structural topping ................................................................................ 154 
5.3.2 Floors without topping ................................................................................................ 154 
5.4 Potential failure modes ........................................................................................................ 155 
5.4.1 Displacement incompatibility between lateral force resisting systems and 
precast floor diaphragms ............................................................................................. 155 
5.4.2 Interaction between precast prestressed units and beams in frame systems . 156 
5.4.3 Possible support loss of hollow core units from a beam due to seismic 
excitation ........................................................................................................................................ 158 
5.4.4 Negative moment failure near to the support ....................................................... 160 
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6 Building physics.............................................................................................................................. 162 
6.1 Thermal performances......................................................................................................... 162 
6.1.1 Thermal insulation ........................................................................................................ 162 
6.1.2 Thermal bridges in cantilevers ................................................................................... 163 
6.1.3 Thermal active floors ................................................................................................... 163 
6.2 Acoustic insulation ................................................................................................................165 
6.2.1 General............................................................................................................................ 165 
6.2.2 Acoustic insulation properties ................................................................................... 165 
7 Environmental aspects ................................................................................................................. 167 
7.1 Optimal use of raw materials ............................................................................................. 167 
7.2 Controlled manufacture ...................................................................................................... 167 
7.3 Recycling of fresh and hardened concrete ...................................................................... 167 
7.4 Closed production system .................................................................................................. 168 
8 Design considerations regarding manufacture ....................................................................... 170 
8.1 During casting ........................................................................................................................ 170 
8.2 Immediately after casting ..................................................................................................... 170 
8.3 Sawing of units ....................................................................................................................... 170 
8.4 Lifting of units......................................................................................................................... 170 
8.4.1 Lifting clamps ................................................................................................................. 171 
8.4.2 Cast-in lifting hooks ..................................................................................................... 171 
8.4.3 Lifting anchor system ................................................................................................... 172 
8.4.4 Lifting chains through slab holes (Ermib system) ................................................... 173 
8.4.5 Blocking rods ................................................................................................................. 174 
8.4.6 Lifting forks..................................................................................................................... 175 
8.4.7 Chains .............................................................................................................................. 175 
8.5 Storage ..................................................................................................................................... 176 
9 Design aspects regarding finished elements............................................................................ 177 
9.1 Dimensional tolerances ....................................................................................................... 177 
9.1.1 Tolerances with regard to structural safety and constructional purposes. ..... 178 
9.2 Slippage of prestressing tendons ....................................................................................... 179 
9.3 Imperfections ......................................................................................................................... 182 
9.4 Weep holes ............................................................................................................................ 183 
9.5 Repair and retrofitting ......................................................................................................... 184 
9.5.1 Preparation of the interface ....................................................................................... 184 
9.5.2 Selection of the repair material ................................................................................. 185 
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9.5.3 Finishing ........................................................................................................................... 185 
9.5.4 Example of application ................................................................................................. 185 
9.6 Test methods ......................................................................................................................... 186 
9.6.1 Tests on hardened concrete ...................................................................................... 186 
9.6.2 Element dimensions and surface characteristics .................................................... 187 
9.6.3 Full scale loading test ................................................................................................... 188 
10 References and Literature .......................................................................................................... 196 
 
 
 
Task Group DRAFT 
Symbols 
 
Roman lower-case letters 
a peak acceleration 
a support length 
αℓ = lx/lpt2 
a0 dynamic coefficient 
b width of precast unit 
bid width of the idealized box section p. 47 
btop width across the top of the unit (narrower than at the bottom) 
bw total web width at the centroidal axis 
bw,in width inner webs 
bw,out width outer webs 
bw(y) total web width at the height y 
bw(z0) total width of the internal webs at the cross-section (z0). 
d effective depth of the hollow core cross-section 
dg max. aggregate size 
e eccentricity of tendon force with respect of the centroidal axis 
eo eccentricity of the prestressing steel p. 28 
fbpd bond strength for anchorage in the ultimate limit state 
fck characteristic (5%) 28 day compressive cylinder strength 
fck,cube characteristic (5%) 28 day compressive cube strength 
fcm mean compressive strength at 28 days 
fctd design value of the tensile strength of the concrete, expressed as fctk0.05/γc 
fctk characteristic axial tensile strength of concrete 
fctk0.05 lower 5% fractile from fctk 
fctm mean concrete tensile strength 
fpd design value of the prestressing strength fp0.1k/γs 
fp0.1k is the minimum 0.1 proof stress 
fn natural frequency of element 
Task Group DRAFT 
h total member depth 
ht,bottom smallest thickness of the bottom flange of the hollow core slab 
htop thickness of the topping 
ht,top is the minimum thickness of the top flange 
k is the core radius 
k load distribution factor 
kc coefficient which takes account of the nature of the stress distribution within the 
section immediately prior to cracking and of the change of the lever arm 
ℓbpd total anchorage length in the ultimate limit state 
ℓpt basic value of the transmission length 
ℓpt1 lower design value of the transmission length (= 0.8 ℓpt) 
ℓpt2 upper design value of the transmission length (= 1.2 ℓpt) 
qk characteristic value of a line load 
ti wall thickness 
u perimeter of the concentrated load with the rectangular loading area 
ui perimeter of the cross-section 
wbot section modulus of the bottom fiber p. 29 
 
Roman capital letters 
 
A concrete cross-section area ? p.52 
 homogenized cross section area ? 
 idealized cross-section ? p. 36 
Ac concrete cross-section area p. 37 
Acp cross-section area above the position z with respect of the centroidal axis 
Act area of concrete within tensile zone 
Ap area of the prestressing tendons 
At torsional core area 
C torsional rigidity 
D maximum width of the core 
Ecm mean value of modulus of elasticity of concrete 
Task Group DRAFT 
Ep modulus of elasticity of the prestressing steel 
Fcr absolute value of the tensile force within the flange immediately prior to cracking 
due to the cracking moment calculated with fct,eff 
Fk,point characteristic value of point load 
Flin,d design value of linear load 
Fpoint,d design value of point load 
Ftop transverse shear force taken by the topping reinforcement of the slabs 
Fweb transverse shear force taken by the webs of the slabs 
G shear modulus 
I second moment of area ofthe cross section with respect to the centroidal axis 
KT cross-sectional factor for torsional rigidity 
L length precast unit 
Lcf distance between the moment zero points 
Lw impact sound reduction index 
MEd design value of total bending moment due to the vertical load 
MEk value of the span bending moment corresponding to the characteristic load 
combination for SLS 
Mx bending moment due to self-weight and external loading at cross-section x 
NEd design value of axial force in the cross-section due to loading or prestressing 
Nr total tensile force acting over the entire tensile stress area 
Nrestr maximum axial restraint force 
P0 harmonic walking force 
Pr prestressing force in tendons at release 
P0 initial prestressing force just after release 
Ppo final prestressing force in tendons after all loses 
PReq required tendon anchorage force 
Pt prestressing force in the considered tendon layer 
Px tendon force at the location along the slab (positive value) 
R’w air borne sound reduction index 
Scp first moment of area above and about the centroidal axis for the homogeneous 
cross-section 
Task Group DRAFT 
Scp(z0) first moment of area above and about the centroid axis in the cross-section (z0). 
T torsional moment 
Vx shear force in the cross-section considered at location x. 
VRdc,st design value of the shear tension capacity 
VRdc,sf design value of shear flexure capacity 
VR1 shear tension capacity of the internal webs 
W total weight of floor. 
WT torsion modulus of the cross-section 
Yc height of the centroidal axis 
ZB, ZT section modulus at bottom and top fibre 
 
Greek lower-case letters 
 
β dynamic modal damping force 
ηMV utilization level for the interaction between bending moment and shear flexure 
µ frictional coefficient 
ν Poisson’s ratio 
σcp concrete compressive stress at the centroidal axis due to axial loading and 
 prestressing (NEd > 0 in compression) 
σpo prestress after initial losses p. 30, 199 
σps tensile stress in the prestressing steel 
σct concrete tensile stress 
σsp spalling stress p. 28 
τult ultimate interface shear stress 
φ rotation angle 
φ(t, t0) creep coefficient 
ψ0, ψ2 factors for the combination and quasi-permanent values of live load 
 
 
Task Group DRAFT 
Terms and definitions 
 
 
Bursting stresses Stresses caused by the prestressing force being applied on the unit 
and occur at a certain distance from the slab end and are 
perpendicular to the tendon axis 
Camber The deflection that occurs in prestressed concrete elements due to 
the net bending resulting from an eccentric prestressing force (it 
does not include dimensional inaccuracies) 
Core Longitudinal void produced by specific industrial manufacturing 
techniques, located with a regular pattern and the shape of which is 
such that the vertical loading applied on the slab is transmitted to the 
webs 
Debonding Wrapping, sheathing, or coating prestressing strand to prevent bond 
between strand and surrounding concrete. 
Diaphragm A horizontal or nearly horizontal system, including a horizontal 
bracing system, acting to transmit horizontal forces to the vertical 
elements resisting the horizontal forces. 
Extrusion technique A very low slump concrete is pressed by screws into the required 
cross-section. The concrete is compacted by vibration in 
combination with pressure. 
Fixings The hardware component of connections. Fixings provide for load 
transfer between the members being connected. 
Floor field A floor slab where each floor unit is designed as part of the whole 
floor, allowing lateral spreading of isolated point or wall loads, and 
spreading of section properties due to the loss of a hole for example. 
Floor slab Several floor units structurally tied together to form a floor area, 
with each unit designed in isolation usually for uniformly distributed 
loading. 
Floor unit A discrete element designed in isolation of other units 
Hollow core floor Floor made of hollow core slabs after the grouting of the joints 
Hogging moment Bending moment inducing tensile stresses in the top fibers (negative 
moment) 
Hollow core unit Monolithic prestressed or reinforced concrete element with a 
constant transversal depth divided into an upper and a lower flange, 
linked by vertical webs, so constituting cores as longitudinal voids, 
the cross-section of which is constant and presents one symmetrical 
axis 
Task Group DRAFT 
 
 
Figure 0-1: Example of a hollow core slab unit 
 
Lateral joints Lateral profile on the longitudinal edges of a hollow core slab shaped 
so to allow grouting between two adjacent slabs 
NDP National Determined Parameters: Parameter to be defined nationally 
(for Eurocodes) to obtain the desired level of safety. The present 
document gives recommended values only 
Non-rigid supports Slabs supported on beams with moderate stiffness, causing a 
composite action between slab and beam, through which stresses 
are introduced in the transversal direction of the slabs 
Protruding strands Projecting strands at the end face of the hollow core units realized 
during manufacture by manual or semi-automatic removal of a strip 
of fresh concrete with a width of two times the required strand 
protruding length. 
Sagging moment Bending moment inducing tension in the bottom fiber (positive 
moment). 
Screed Non-structural cast in-situ concrete or mortar layer used to level 
the upper face of the finished floor. 
Shear-flexure Failure mode when a flexural crack develops into a shear crack 
Shear tension Brittle shear failure mode in the region uncracked in flexure, if the 
principal tensile stress in the web at about mid-depth reaches the 
tensile strength of the concrete 
Slipform technique A higher slump fresh concrete is fed around steel formers. A profiled 
form is moved during production and the concrete is compacted by 
vibration around these forms. 
Spalling stress Stress along the end face of prestressed units and are due to vertical 
tensile stresses in the end zone of the element 
Splitting stress Circumferential stress that are caused by the component of the bond 
action that is perpendicular to the tendon axis. 
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Topping Cast in-situ reinforced concrete layer on the hollow core slab 
intended primarily to increase the capacity. 
Vierendeel effect A truss beam floor diaphragm model composed of rigid top and 
bottom flanges interconnected by vertical struts, restrained by the 
flanges of the hollow core units. 
Web Vertical concrete part between two adjacent cores (internal webs) 
or on the lateral edges of the slab (outermost webs) 
Wet cast Conventional concrete process, as opposed to those used in hollow 
core, concrete block, some pipe manufacturing techniques and the 
like, which are dry cast processes. 
 
 
Task Group DRAFT 
Task Group DRAFT 
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1 Introduction 
 
Hollow core units are now the most widely used type of precast flooring in Europe 
representing 40 to 60% of the precast flooring market. This success is largely due to the 
highly efficient design and production methods, choice of unit depth and capacity, surface finish 
and structural efficiency, but also in other features such as optimum use of materials, 
slenderness and speed of construction, environmental friendliness, etc. 
Hollow core floors are mainly used for floors and roofs of buildings with spans from 5 to 20 
meters and more, such as office buildings, hospitals, schools, shopping area, parking garages 
(car parks), industrial buildings, etc. Another frequent application is for apartment buildings 
and housing because of the favorable cost rate and the fast erection. The units are mostly 
prestressed using a single layer of tendons, but around 10% of the units used in housing and 
for short spans may be statically reinforced. Hollow core slab systems can also provide slabs 
to be used as walls. The hollow core wall panels are then symmetrically prestressed withtwo 
layers of tendons. 
The units are manufactured using a long line production method, using or slip-forming 
machines which forms the voids (or ‘hollow cores’), cured and cut to the desired length within 
24 hours, transported and erected on site onto concrete, steelwork, timber or masonry 
supports, as shown in Figure 1-1. Hollow core units can also be manufactured by casting 
concrete directly into molds with void formers creating the cores. 
 
Figure 1-1: Factory storage of prestressed hollow core unit and installation on site. 
In 1988 the FIP Commission on Prefabrication has published recommendations for the design 
of prestressed hollow core floors [20]. They were intended to complement the CEB-FIP 
Model Code 1990 [24] and have been used as a basis for national and international standards, 
for example the Eurocode 2 – Chapter Prefabrication [3] and the European CEN Product 
Standard EN 1168 [5]. 
Since the first publication of the FIP Recommendations in 1988, the knowledge on the 
performances of prestressed hollow core floors in various applications has progressed in an 
important way. The depth of the hollow core slabs has also increased. A number of new topics 
have already been dealt with in two complementary reports, namely the FIP Guide to good 
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practice on "Composite floor structures" in 1998 [22], and the fib Bulletin N° 6 "Special design 
considerations for prestressed hollow core floors" in 2000 [15]. New items have been studied 
recently such as: Shear and torsion interaction; Design for large openings; Fire resistance, and 
more. 
These reports can be considered as basic documents for the specific domains. The FIP 
Recommendations from 1988 focused mainly on extruded hollow core slabs (drawings, 
photos etc.) generally of between 150 mm and 320 mm depth and was complemented by data 
from slipformed units. As the depth of the units has increased up to 550 mm and new 
developments are ongoing for depths up to 1000 mm, new design rules are needed. The clear 
majority of hollow core units are 1200 mm wide, but 1500 mm and 2400 mm widths are made 
and even 3600 mm width has successfully been used in special projects. 
The present document is intended to complement and update the FIP Recommendations 1988 
with the knowledge of today. However, further research is still ongoing, which means that 
the present design rules should not inhibit further evolution and increase and accept hollow 
core floors in new type of structures. 
Scope 
The application of this document is limited to prestressed units with a maximum depth of 
500 mm and a maximum width of 1200 mm. The units may be used in composite action with 
a cast in-situ structural topping. This document does not cover the design of trimmer beams. 
 
Figure 1-2: Hollow core unit 500 mm depth 
 
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2 General information 
2.1 Product description 
 
Hollow core units are normally used as simply supported one-way spanning floor slabs. They 
can also be used with cantilever and continuous supports, and as wall panels. The units are 
pretensioned with bottom and occasionally top tendons, consisting of individual wires or 
helical strands, and do not have any shear or transverse reinforcement. Strand systems and 
arrangements may vary a lot depending on the production system and the practices of each 
producer. 
The longitudinal edges of the units are profiled with a ‘shear key’ as shown in Figure 2-1, to 
ensure the adequate transfer of horizontal and vertical shear between adjacent units. The 
units are cast mainly on steel beds between 80 m and 180 m long and later cut to length using 
a circular saw. A square end is standard but skew ends, which are necessary in a 
non-rectangular layout, may be specified. Longitudinal cutting is possible for so-called ‘fitting 
slabs’ where widths narrower than 1200 mm are required to suit the floor layout. By inserting 
one or two formers into standard width production 400 mm or 600 mm widths can be 
standardized. 
Slabs are made of normal concrete, typically grade C40/50 to C50/60 with a density of 
24-25 kN/m3. 
 
2.1.1 Cross-sections 
 
Prestressed hollow core units are slabs with constant depth and longitudinal cores of which 
the main purpose is to reduce the weight of the floor. The elements are available in different 
depths to satisfy the various performance needs for span and loading. The most popular 
depths are 150, 200, 250, 300, 400 mm, but other depths such as 265, 320, 350, 450, 500 and 
550 mm are available in some countries. Typical cross-sections are shown in Figure 2-1. The 
void percentage (volume of voids to total volume of solid slab of equal depth) is between 30% 
and 50%. 
Prestressed hollow core units are nominally 1200 mm wide, originating in the 1950’s from 4 
feet and 1.2 m widths in the USA and Europe as shown in Figure 2-1. The actual unit width is 
usually 3 to 6 mm less than the nominal size to allow for constructional tolerances and 
prevents overrunning of the floor layout due to cumulative over width. 
 
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Figure 2-1: Typical cross-section of hollow core slabs 
The shape of the voids is usually circular, oval or parallel sided with triangular and/or semi-
circular ends, as illustrated in Figure 2-1 and Figure 2-5. 
 
2.1.2 Fitting slabs 
 
The most cost-effective use of hollow core slabs requires a modular grid building system 
(12M=1200mm). The system may also include 3M modules. However, where exact 
modulation is not possible it may be necessary to produce a smaller unit, cut to the desired 
width from a standard module (see Figure 2-3). Narrow strips of in-situ cast concrete may 
also be used. In many cases this in-situ strip can be usefully incorporated into the connection 
and tying system. 
Non-standard units with a width less than 1200 mm are cut in the green concrete during 
casting of the line. The place of the longitudinal cut should correspond to the location of a 
longitudinal core. Normally, the fitting slab (or the remaining usable part of a cut slab) must 
be at least 400 mm wide. The width of the fitting slab should possibly be designed so that both 
pieces of the cut slab can be used. This way the waste is minimized. It should be noted that a 
cut edge does not have the same edge profile as a regular slab. Edges cut in fresh concrete 
are rough. If a straight edge is needed, the slabs are sawn after hardening. 
In the absence of a structural topping, fitting slabs should preferably not be located at the edge 
of the floor, especially when the floor slab is connected to a wall. The reason lies in the 
reduced lateral stiffness of a narrower fitting slab. 
 
Figure 2-2: fitting slab between two 'standard' slabs 
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c 
Figure 2-3: Example of a floor with fitting slab 
 
2.1.3 Geometrical flexibility 
The geometry from a hollow core slab can be adjusted according the practical needs of almost 
every construction site. Skew ends are made by cutting the slab in a similar way as the fitting 
slabs as described above. A minimum top-angle of 30° (fig ) should be respected to avoid 
cracking. Openings and cut outs are mainly made in the fresh concrete. In general, openings 
and cut outs should be realized in the factory in order to avoid inappropriate cutting and 
damage of the strands. 
 
Figure 2-4: example of a floor with elements containing different kind of opening and cut outs 
 
2.2 Methods of manufacture 
The production of prestressed concrete hollow floor elements is highly mechanized. The units 
are manufactured using the long line extrusion or slip-forming technique. In the extrusion 
system, a very low slump concrete (water-cement ratio approx. 0.35) is pressed by screws 
into the required cross-section. The cores are formed with short augers or tubes. In the slip 
https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwjV1b_rrqLeAhVNxhoKHUMyCVsQjRx6BAgBEAU&url=http://civilengineersforum.com/hollow-core-slab-advantages/&psig=AOvVaw346ZBIKAdG5rWxN-UjoPIi&ust=1540583482437316Task Group DRAFT 
6 
form technique, the manufacture is done by feeding a higher slump fresh concrete around 
steel formers (W/C approx. 0.42). A single profiled form is moving along a stationary bed 
during production and the concrete is compacted by vibration around these forms. 
Alternatively, the machine is stationary and the bed, together with the tendons, moves 
beneath the machine. The shape of the formers is designed to give the optimal flexural and 
shear performance as well as providing adequate cover to the prestressing tendons. 
 
Figure 2-5: Typical shapes of voids 
The steel or sometimes concrete beds are usually 1200 mm wide and about 80 to 180 m long. 
The degree of prestressing, tendon pattern and depth of units are the main design parameters. 
 
Figure 2-6: Example of production hall for prestressed hollow core elements 
In some countries so called “wet-cast elements” are used. These elements are characterized 
by large square (or rectangular) voids formed by placing polystyrene (or similar lightweight 
materials) blocks onto the bottom flange during a two-stage pour. Figure 2-7 shows a typical 
cross section of wet-cast units, in which the 50 mm thick bottom flange contains up to 15 
strands (typically 9.3 mm dia. stressed to 70% · Pyk = 1770 N/mm2). This is poured and 
compacted first. After the void formers have been laid and secured against buoyancy, as shown 
in Figure 2-8, the internal webs and top flanges are cast and compacted ensuring that the two 
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layers are made homogenous by a mechanical intervention across the interface. Depths range 
from 150 to 300 mm. Concrete strength is fck = 50 N/mm2 and fc = 35 N/mm2 (cube) at transfer 
at 18 hours. The slabs contain 5 cores generally, but only 3 where lifting pins/hooks are located 
and are cast solid for 500 mm at each end (Figure 2-8). Holes, notches and slots for tie bars 
are easily formed by additional polystyrene blocks. 
 
Figure 2-7: Cross section of wet-cast hollow core unit with polystyrene void formers 
 
Figure 2-8: Placing polystyrene void formers onto 1st poured bottom flange. 
 
Concrete is specified as a 28 day characteristic compressive cylinder strength fck. The mean 
strength is taken as fcm = fck + 8 N/mm2. Cube strength fck,cube is used in many factories for the 
convenience of testing cubes. The specified grade fck is typically C45/55 for slip-formed units 
and C45/55 to C50/60 for extruded units, although the strength of locally available aggregates 
and cement may dictate otherwise. The corresponding concrete strength class at detensioning 
(called transfer) of the tendons at time t of between 8 and 24 hours is C25/30 to C30/40. 
The tensile strength of the concrete is important at detensioning. Since in hollow core units 
the tendons cannot be debonded or deflected, the limiting pretensioning is often controlled 
by tension at the top of the unit during detensioning operations. 
The cement is usually rapid hardening Type I of grade 42.5R or 52.5R and may contain a small 
content of pozzolana (e.g. pulverized fuel ash according to the supply of these waste 
materials). Aggregates are most limestone or gravel, with crushed granite or greywacke used 
in some countries, 10 to 14 mm size. Fine aggregates consist of rushed rock or gravel or 
natural sand of 4 – 5 mm size. Small quantities of admixtures, such as air entrainment agents, 
are used to increase plasticity and reduce water content in slip-formed units. 
Prestressing strands and wires are used with the following properties: 
a) Strands 
- fpk = 1860 N/mm² or 1770 N/mm² characteristic strength 
- Modulus of elasticity may be taken as 195 kN/mm² 
- Dimensions: 
Task Group DRAFT 
8 
 ϕ 5.9 mm cross-section 21.2 mm² 3 ϕ 3 wire 
 6.9 mm 29 mm² 7-wire strand 
 9.3 mm 52 mm² 7-wire strand 
 12.5 mm 93 mm² 7-wire strand 
 12.9 mm 100 mm² 7-wire strand 
 15.2 mm 139 mm² 7-wire strand 
 
- Other cross-sections such as 3-wire strand are possible 
 
b) Wires 
- fpk = 1670 N/mm² (ϕ 7 mm) or 1770 N/mm² characteristic strength 
- Modulus of elasticity may be taken as 205 kN/mm² 
- Dimensions: 
ϕ 5 mm cross-section 19.6 mm² 
 7 mm 38.5 mm² 
 9 mm 63.5 mm² 
 
Additional requirements concerning the minimum 0.1% proof stress fp0.1k , relaxation level 
after 1000 h, etc., are available in EN 10138-2 , Prestressing steel - Part 2: Stress relieved 
cold drawn wire [7], and in EN10138-3 (under technical review) Prestressing steels - Part: 3 
Strands [8], or in equivalent National Standards. 
 
2.3 Design methodology 
2.3.1 Procedure 
 
The design and calculation of hollow core floors and roofs is carried out in two steps namely 
the design of the individual slab units and the design of the complete floor. 
The individual slab units are dimensioned with respect to flexural capacity and shear resistance 
and may or may not be in combination with torsion when applicable. A further check 
concerns cracking due to bending. The punching shear resistance for high-concentrated loads 
must also be checked. Finally, the deflection is calculated and limited to recommended values. 
Other design criteria include fire resistance, acoustic and thermal performance, durability, 
handling and construction methods. 
While the design of the whole precast floor structure concerns the analysis of bending 
moment and shear force capacities, the most important aspect is to achieve a stable and 
coherent structure out of individual units. The most important objectives are: 
- structural integrity 
- diaphragm action of the floor or roof for the transmission of horizontal actions 
- transverse distribution of concentrated or linear loads 
Task Group DRAFT 
9 
 
 
2.3.2 Design parameters 
 
The design parameters in this document are based on the ‘Partial Factor’ method, given in EN 
1990 Section 6 [1]. Numerical values for partial factors and other reliability parameters for 
materials and products are recommended in the Eurocodes as basic values that provide an 
acceptable level of reliability. They have been selected assuming that an appropriate level of 
workmanship and of quality management applies. In the EU, each member state can give 
different values in National Annexes (National Determined Parameters - NDP’s). 
γc is the partial safety factor for concrete. The recommended value in Eurocode 2 [3] is 1.5, 
but in prefabrication with a certified quality assurance system, γc = 1.4 is justified. γs is the 
partial safety factor for steel tendons taken as 1.15. 
 
Task Group DRAFT 
10 
3 Design of the cross-section 
3.1 General 
The main structural functions of floors are span-load bearing, transverse distribution of 
vertical loads, diaphragm distribution of horizontal actions and resistance against fire and 
accidental actions on the floor elements or supporting structure. In precast floors, individual 
slab units are assembled and connected to form a complete floor. Two main factors influence 
the design of floors composed of precast prestressed hollow core units: 
a) Generally, prestressed hollow core units have no reinforcement other than the 
longitudinal prestressing tendons anchored by bond. Owing to the absence of 
complementary reinforcement at the support and in the transverse direction, the tensile 
strength of the concrete has to be taken into account for the determination of the shear 
capacity, load distribution etc. 
b) Because of the specific manufacturing methods, it is in most cases difficult to produce the 
units with directly anchored tie bars or welded plates. This applies also to stirrups 
protruding from the joint surfaces. Therefore, standard solutions for connections in 
precast construction can seldom be adopted for hollow core floors. 
Intensive field experience gathered from all over the world, and extensive research have 
learned that prestressed hollow core floors are perfectly able to fulfil all the required 
structural functions, on condition that someelementary design principles are met. 
 
3.2 Minimum thickness of webs and flanges 
The nominal thickness specified on the drawings shall be at least the minimum thickness 
increased by the maximum deviation (minus tolerance) declared by the manufacturer. 
The minimum thickness shall be: 
- for any web, not less than the largest of h/10, 20 mm and (dg + 5 mm), where dg and h 
are in millimeters; 
- for any flange, not less than the largest value of √2h, 17 mm and (dg + 5 mm), where 
dg and h are in millimeters; however for the upper flange, not less than 0.25 bc, where 
bc is the width of that part of the flange in which the greatest thickness is not greater 
than 1.2 times the smallest thickness (see Figure 3-1). 
 
Figure 3-1: Minimum thickness of upper flange hf,top ≥ 0.25 bc 
Task Group DRAFT 
11 
 
 
 
3.3 Basic design principle 
 
Because prestressing tendons in hollow core units are anchored by bond, the transfer of the 
prestressing force in the concrete occurs over a certain distance, called the transfer length. 
Since this zone is situated at the support of the slab, and owing to the absence of 
complementary reinforcement in the units at the support and in the transverse direction, the 
tensile strength of the concrete has to be taken into account for the determination of the 
shear capacity, load distribution, etc. 
The tensile strength of concrete can be considered on condition that local imperfections, due 
to scatter in the concrete quality or local damage, are compensated by the redistributing 
capacity of the member itself or the structural floor system as a whole. 
The redistributing capacity of loads in a hollow core floor can be achieved in the following 
ways: 
- a reinforced peripheral beam; 
- a structural reinforced topping; 
- friction between the hollow core slab and the supporting structure. 
 
a) Reinforced peripheral beam 
The main function of a peripheral beam (and internal beam in multi-bay floors), together with 
coupling bars anchored into hollow cores as shown in Figure 3-2, is to limit the lateral 
displacement of the hollow core units, to enable the longitudinal joints to take up vertical 
shear forces. Details about the practical design of a peripheral tie beam are given in Sections 
4.2.2.1. 
Task Group DRAFT 
12 
 
Figure 3-2: Main function of peripheral and internal beams to form a slab field by connecting hollow core floor 
units via reinforced concrete beams and shear keys. 
b) Structural reinforced topping 
The load distribution is also achieved using a structural topping. Guidelines about the design 
are given in Section 4.5. 
 
c) Friction 
Friction may be used to achieve limitation of lateral displacements in case of small spans and 
limited loading, as for example in housing structures. Relying on friction at the supports is 
only allowed in non-seismic situations. 
An additional condition for design on the basis of tensile strength of concrete is that no 
significant axial tensile forces are present, for example due to restrained deformations that 
may occur. 
 
3.4 Prestressing 
3.4.1 Transfer of prestressing 
After release and the sawing into individual units, the transfer of the prestress to the concrete 
is, according to Eurocode 2, Figure 8.17 [3], a linear build-up of prestress. Other national 
codes use a parabolic build up. There is no special anchorage demand along the transfer length 
(also known as transmission length or zone) as long as the slab section is without bending 
cracks. Strain gradients over the height of the cross-section due to bending and shear are the 
same for the concrete cross-section and the tendons assuming full strain compatibility. The 
method suggested in Eurocode 2, equation 8.21 [3] requires no further anchorage capacity in 
the transfer zone (x < lpt) than for the prestressing force. Figure 3-3(same as Figure 8.17 of 
Task Group DRAFT 
13 
 
EC2) presents the build-up of the prestress (in the abscissa) versus the ultimate anchored 
capacity at the end of a tendon (in the ordinate). 
 
Figure 3-3: Stresses in the anchorage zone of pre-tensioned members: (1) at release of tendons, (2) at ultimate 
limit state -(Fig 8.17 from EN 1992-1.1) 
 
 
3.4.2 Stresses in the transmission zone 
 
In the transmission zone (x < lpt) of pretensioned members, three types of tensile stresses 
should be distinguished: splitting, spalling and bursting as shown in Figure 3-4. Splitting stresses 
are circumferential stresses that are caused by the component of the bond action that is 
perpendicular to the tendon axis. Spalling stresses appear along the end face of the member 
and reach a maximum at some distance from the slab end. Bursting stresses occur also at a 
certain distance from the slab end. They are perpendicular to the tendon axis, and the 
maximum stress occurs near the tendon(s). 
 
Task Group DRAFT 
14 
 
Figure 3-4: Stresses in the transmission zone. Note that the data in the Figures are based on tests on hollow 
core units up to 320 mm thickness. 
 
Bursting and spalling are related to the distribution of the prestressing force over the total 
cross-section, splitting is due to bond action. Bursting and splitting stresses occur in the same 
region, therefore they should be superimposed in the analysis of the stress state. 
 
Figure 3-5: spalling cracks 
Stresses in the ends of a hollow core unit may be analyzed by finite element method. Stress 
analyses of this type have been carried out at the Technical Research Centre of Finland, at 
the Technical University of Gothenburg in Sweden and at the Technical University of 
Darmstadt in Germany. The stress analysis gives indicative figures for the tensile stresses 
acting on a cross section at various distances from the end of the slab. The risk of cracking 
can be analyzed by comparing the average tensile stresses in the webs with the experimentally 
measured tensile strength of the concrete. The results of such stress analyses have been used 
to determine the cross-section profiles, minimum web thickness and maximum allowable 
prestressing forces for hollow core slabs of various cross-sections. 
An approximate idea of the cracking forces in the end of the slab can be obtained using the 
method presented in the FIP Recommendations [20] and which was updated in EN1168 [5]. 
If the result indicates that there is a danger of cracking, a more exact analysis should be carried 
out using the finite element method of stress analysis or by tests. 
Task Group DRAFT 
15 
 
EN1168 gives the following equation for the calculation of the spalling stress σsp. The formula 
was developed at the time where the experience was limited to a depth of 320 mm. 
For the web in which the highest spalling stress will be generated, or, for the whole section if 
the strands or wires are essentially well distributed over the width of the element, the spalling 
stress σsp shall satisfy the following condition: 
 
 
 𝜎𝜎𝑠𝑠𝑠𝑠 ≤ 𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐(𝑡𝑡0) (3-1) 
with 
 
𝜎𝜎𝑠𝑠𝑠𝑠 =
𝑃𝑃𝑐𝑐0
𝑏𝑏𝑤𝑤,𝑖𝑖 ∙ 𝑧𝑧𝑐𝑐𝑠𝑠
∙
15𝛼𝛼𝑒𝑒2.3 + 0.07
1 + �
𝑙𝑙𝑠𝑠𝑐𝑐,1
𝑧𝑧𝑐𝑐𝑠𝑠
� ∙ (1.3 ∙ 𝛼𝛼𝑒𝑒 + 0.1)
 (3-2) 
and 
𝛼𝛼𝑒𝑒 =
�𝑧𝑧𝑐𝑐𝑠𝑠 − 𝑘𝑘�
ℎ
 
 
(3-3) 
 
fctm is the value of the tensile strength of the concrete deduced at the time that the 
prestress is released based on tests; 
Pmo is the initial prestressing force just after release in the considered web or the total 
prestressing force of the slab in case of solid slabs; 
bw,i is the thickness of the individual web (or the total width b of the slab in case of a 
solid slab); 
zcp is the eccentricity of the prestressing steel; 
lpt1 is the lower design value of the transmission length; 
k is the core radius taken equal to the ratio of the section modulus of the top fiber 
and the net area of the cross section (Wtop/Ac); 
 
3.5 Checks in Ultimate Limite State 
 
3.5.1 Flexural capacity 
3.5.1.1 General approach to flexural capacityThe ultimate flexural bearing capacity of hollow core slabs should be determined in the 
classical way according to the provisions of Eurocode 2 [3] or the standard in the place of 
use. When a structural topping is applied, the flexural bearing capacity is calculated for the 
composite section considering the high tensile steel reinforcement located in the topping 
which should be properly anchored. When no structural topping is applied, for negative 
moments due to restraint at the support, it is allowable to take advantage of normal 
Task Group DRAFT 
16 
reinforcement anchored in concreted cores or grouted joints if the floor is arranged and 
detailed according to Sections 4.10 and 4.14.2.4. 
The ultimate limit states for hollow core units with structural topping can be calculated as 
composite sections, subject to fulfilling the requirements for shear at the interface. 
3.5.1.2 Calculation of ultimate moment of resistance MRd 
 
𝑀𝑀𝑅𝑅𝑅𝑅 = �𝜎𝜎𝑠𝑠𝑅𝑅 ∙ 𝐴𝐴𝑠𝑠 ∙ 𝑧𝑧 (3-4) 
 
where 
Ap is the area of tendons in the tension zone; 
z is the internal lever arm; 
dn is the depth to centroid of concrete in compression. If the depth to the neutral axis 
x lies below the top of the hollow cores curve fitting for the shape of the 
compression area is required as shown in Figure 3.6-1; 
σpd is the stress in tendons satisfying force equilibrium between the tendons Fs and 
concrete Fc, and strain compatibility of the ultimate failure strain in the concrete 
εcu3 = 0.0035 and the strain in the tendons, which includes pre-strain εpo = σpmo / Ep 
due to prestress σpmo after initial losses. 
 
3.5.2 Anchorage 
To guarantee the bearing capacity of the member it must be verified that the prestressing 
steel is well anchored under the design load. Two possible failure modes should be checked: 
- anchorage capacity of a pretensioned tendon in the transfer region without cracks; 
- anchorage capacity of a tendon for the transfer of the tensile force over a possible 
bending crack, and for the transfer of the additional tensile force component from an 
inclined shear bending crack. 
For a simply supported hollow core unit the first bending crack starts in the position where 
the tensile stress in the bottom fiber reaches the tensile strength of the concrete. The 
formation of a crack gives a sudden increase of the tensile force in the tendon as the tensile 
stresses in the un-cracked concrete cross-section need to be passed over the crack by the 
tendon. This increased tendon force needs to be fully anchored to avoid a sudden failure at 
crack formation. 
Further increase of the load results in the formation of new bending cracks closer to the slab 
support. Each new bending crack starts from the bottom surface and if shear-forces are 
present, the crack turns off in a typical inclined bending shear crack. These inclined cracks 
result in an increased demand of the tendon force as the loaded region on the un-cracked 
upper part extends further from the support compared to the location of the bending crack 
Task Group DRAFT 
17 
 
on the bottom surface. A smaller angle between the inclined crack and the slab axis results in 
further increase of the tendon force. 
A conservative approach is suggested by using a small inclination of the shear bending crack. 
The proposed increase (1.5· Vx ) of the tensile force to be anchored corresponds to an 
inclination of 18.4 degrees. This results in the following force to be anchored: 
 
 
𝑃𝑃𝑅𝑅𝑒𝑒𝑅𝑅 =
𝑀𝑀𝑥𝑥
0.9 ∙ 𝑑𝑑
+ 1.5 ∙ 𝑉𝑉𝑥𝑥 (3-5) 
 
 
where d is the effective depth of the cross-section and the subscript x indicate that the bending 
moment M and shearing force V are evaluated at different positions x from the support. 
In some cases it might be more convenient to express the tensile capacity needed at a position 
‘x’ from the support, by calculating the bending moment at a position shifted further from the 
support. A shifting distance of 1.35· d is proposed in the following alternative expression for 
the demanded anchorage capacity: 
 
 
𝑃𝑃𝑥𝑥,𝑟𝑟𝑒𝑒𝑅𝑅 = 𝑚𝑚𝑚𝑚𝑚𝑚 ��
𝑀𝑀𝑥𝑥,𝑅𝑅(𝑥𝑥 + 1.35 ∙ 𝑑𝑑)
0.9 ∙ 𝑑𝑑
� , �
𝑀𝑀𝑅𝑅,𝑐𝑐𝑚𝑚𝑥𝑥
0.9 ∙ 𝑑𝑑
�� (3-6) 
 
As an alternative, the method suggested by EC2, Section 9.2.1.3 “Curtailment of longitudinal 
tension reinforcement” [3], may be applied. It stipulates that for members without shear 
reinforcement ΔFtd may be estimated by shifting the moment curve a distance d. 
3.5.2.1 Protruding strands 
Precasters in France were confronted with cast in situ projects they had to transform into 
precast projects. In many cases however, the beams were designed for cast in situ 
circumstances. By consequence, precasters were not able to respect the support length as 
prescribed by most common codes. Producers of hollow core elements had to adapt since 
they had no influence at all at the design of the beams. Producers started to produce hollow 
core slabs with provisions to cope with this new situation. When the effective support length 
was lower than 50 mm but still larger than 30 mm, protruding strands were applied. In time, 
French contractors and producers of supporting beam started considering 50 mm support 
length combined with protruding strands as a standard solution where no additional propping 
is needed. 
French designers decided to develop a safe approach and to design the hollow core slabs in 
an alternative way: 
Task Group DRAFT 
18 
- Floors are designed in the same way prestressed floor plates (filigrane slabs) are 
designed; 
- Floors are designed in an isostatic way; 
- Additionally, the support is supposed to resist a moment equal to 30% of the moment 
ad mid-span; 
- The floor has to have a structural topping. 
The structural topping on hollow core floors is generally used since the topping is considered 
to provide for diaphragm action. 
The French industry and authorities developed a full philosophy on the use protruding strands 
and the detailing of the connection. Protruding strands should be used when all relevant 
requirements are respected only. 
 
 
Figure 3-6: The use of hollow core slabs with protruding strands requires additional reinforcement on the 
support. Propping is needed when the effective support length is less than 50 mm. 
 
3.5.3 Shear capacity 
3.5.3.1 General 
As mentioned before, due to the special manufacturing process hollow core units have, in 
general, no reinforcement other than longitudinal prestressing tendons (strands or wires) 
anchored by bond. Strands are placed in one or two layers (sometimes three layers) in the 
bottom region of the webs. In some cases, the elements are also provided with top strands 
or wires in the upper zone of the cross-section. Normally there are no stirrups or other 
shear reinforcement. Consequently, the shear capacity has to be calculated taking into account 
the design tensile strength of concrete fctd. The calculation methods given in this Chapter are 
mainly based on Eurocode 2 [3] but with some extensions to cover the special design 
situations relevant for hollow core units. 
The prestressing force is introduced by bond and the design value of the transfer length is in 
the order of 0.4 to 1.5 m, depending on the prestressing level and the type of tendon. The 
anchorage capacity of the strand is a critical parameter for the design of slabs cracked in 
flexure, less so for wires which have shorter lpt2 due to smaller diameters. 
The problem of cracking in hollow core slab units is especially important with respect to the 
shear resistance. Hence crack formation in the development zone of the prestressing force is 
Task Group DRAFT 
19 
 
unacceptable. If cracking appears where the full prestressing force is developed, considerable 
shear can be resisted by the compressive zone. Furthermore, as the crack is not so deep, the 
crack width will probably stay small, thus enabling considerable interlocking effects. On theother hand, within the development length, a possible crack can be expected to penetrate the 
cross-section almost completely and reach the bottom reinforcement. The remaining shear 
resistance will then depend mainly on possible dowel action of the bottom tendons. Figure 
3-7 illustrates this principle in a classical shear tension failure. 
 
Figure 3-7: Shear tension failure of hollow core unit. 
 
Increase of shear capacity close to the support region, as expressed in Eurocode 2, clause 
6.2.2(6) [3], is not applicable for hollow core units as the strands are not fully anchored at the 
support. 
In shear, 3 modes of failure are considered 
- failure occurring in the region uncracked in bending (shear tension failure), 
- failure occurring in the region cracked in bending (shear flexure failure), 
- anchorage failure. 
Regions uncracked in bending are defined by a flexural tensile stress smaller than fctd. 
Shear tension failure occurs in the region near to the support in regions not cracked in 
bending (zone 1 in Figure 3-8). Diagonal cracks are formed close to the ends of the units 
propagating through the non-prestressed and unreinforced regions of the unit (Figure 3-7). 
This is calculated basically in the same way as suggested in Eurocode 2 equation (6.4) [3] but 
with an extension that includes the effect of longitudinal shear stresses along the strands in 
the transfer region. This extension also considers the vertical location of prestressing tendons. 
In addition to this, the variable width of the hollow core unit over the cross-section height is 
considered when evaluating the maximum principal stress. As this is a failure mode in regions 
not cracked in bending, it is of brittle character. 
Bending shear failure occurs when a flexural crack develops into a shear crack (zone 2 in 
Figure 3-8). The flexural cracking criterion in ULS is fctd. Because of the relatively large amount 
of prestress in hollow core slabs, it is usually the first (or second) flexural crack which causes 
the shear failure. Failure occurs where the shear force exceeds the shear compression 
capacity and a single flexural crack initiates shear failure. 
Task Group DRAFT 
20 
 
Figure 3-8: Cracking zones and pattern in a reinforced or prestressed concrete member 
 
In a general design situation, the shear resistance capacities for the relevant failure modes 
need to be evaluated along the hollow core unit span and in each location compared with 
design values of section forces. If a region close to the support is cracked in bending it is 
essential to check the anchorage capacity for the actual tendon force. 
In a more general situation, the hollow core units may be subjected to an interaction of 
bending, shear and torsion. This in combination with non-rigid supports provided by beam 
elements results in some additional considerations which will be discussed in Sections 3.8, 3.9, 
3.10 and 4.8. 
 
3.5.3.2 Calculation of the shear capacity in the region uncracked in bending 
The European Product Standard for hollow core slabs, EN 1168 [5] specifies the following 
equations for the calculation of the shear capacity in regions uncracked in bending. 
Although design equations are based on the classical elastic analysis τ = VEd S / I bw and the 
appearance of a first crack is when the principal tension exceeds the tensile resistance of the 
concrete in the webs, an ultimate tensile stress fctd used. Referring to Figure 3-9 the shear 
resistance should be calculated with the following expression: 
 
 
𝑉𝑉𝑅𝑅𝑅𝑅𝑐𝑐,𝑠𝑠𝑐𝑐(𝑦𝑦) =
𝐼𝐼 ∙ 𝑏𝑏𝑤𝑤(𝑦𝑦)
S(𝑦𝑦)
��𝑓𝑓𝑐𝑐𝑐𝑐𝑅𝑅2 + 𝜎𝜎𝑐𝑐𝑠𝑠(𝑦𝑦) ∙ 𝑓𝑓𝑐𝑐𝑐𝑐𝑅𝑅 − 𝜏𝜏𝑐𝑐𝑠𝑠(𝑦𝑦)� (3-7) 
with 
 
 𝜎𝜎𝑐𝑐𝑠𝑠(𝑦𝑦) = ���
1
𝐴𝐴
+
(𝑌𝑌𝑐𝑐 − 𝑦𝑦)�𝑌𝑌𝑐𝑐 − 𝑌𝑌𝑠𝑠𝑐𝑐�
𝐼𝐼
� ∙ 𝑃𝑃𝑐𝑐(𝑥𝑥)� −
𝑛𝑛
𝑐𝑐=1
𝑀𝑀𝐸𝐸𝑅𝑅
𝐼𝐼
∙ (𝑌𝑌𝑐𝑐 − 𝑦𝑦) (3-8) 
 (positive if compressive) 
and 
 
𝜏𝜏𝑐𝑐𝑠𝑠(𝑦𝑦) =
1
𝑏𝑏𝑤𝑤(𝑦𝑦)
∙���
𝐴𝐴𝑐𝑐(𝑦𝑦)
𝐴𝐴
−
𝑆𝑆𝑐𝑐(𝑦𝑦) ∙ �𝑌𝑌𝑐𝑐 − 𝑌𝑌𝑠𝑠𝑐𝑐�
𝐼𝐼
+ 𝐶𝐶𝑠𝑠𝑐𝑐(𝑦𝑦)� ∙
𝑑𝑑𝑃𝑃𝑐𝑐(𝑥𝑥)
𝑑𝑑𝑥𝑥
�
𝑛𝑛
𝑐𝑐=1
 (3-9) 
 
Task Group DRAFT 
21 
 
 
 
Equation (3-7) should be applied for all critical points on a straight failure line running from 
the edge of the support with an angle β = 35° with respect to the horizontal axis. The critical 
point is the point on this failure line where the calculation result of VRdc,st is the smallest. 
The definition of symbols is given here after. 
I is the second moment of area of the homogeneous concrete cross section 
bw(y) is the web width at the height y 
Yc is the height of the centroidal axis 
Sc(y) is the first moment of the area above height y and about the centroidal axis 
y is the height of the critical point on the line of failure 
Lx is the distance of the considered point on the line of failure from the starting point 
of the transmission length (= x) 
σcp(y) is the concrete compressive stress at the height y and distance x 
n is the number of tendon layers 
A is the transformed cross section 
Pt(Lx) is the prestressing force in the considered tendon layer at distance x. The transfer 
of prestress shall be taken into account according to 8.10.2.2 of Eurocode 2 [3] 
MEd is the total bending moment, 
τcp(y) is the concrete shear stress due to transmission of prestress at height y and 
distance x 
Ac(y) is the concrete cross-section above height y 
Cpt(y) is a factor taking into account the position of the considered tendon layer 
 Cpt = -1 when y ≤ Ypt 
 Cpt = 0 when y > Ypt 
Ypt is the height position of considered tendon layer 
 
For all above mentioned cross-section parameters, the tendons should be expressed as their 
transformed area according to the long-term modular ratio αE as follows: 
 
𝛼𝛼𝐸𝐸 = 
𝐸𝐸𝑠𝑠
𝐸𝐸𝑐𝑐𝑐𝑐
 (3-10) 
 
Task Group DRAFT 
22 
 
where: 
Ep is the modulus of elasticity of the prestressing steel 
Ecm is the modulus of elasticity of concrete 
 
 
Figure 3-9: Failure line (A) and forces at the considered section (B) 
 
A calculation example is given in fib Bulletin xx, Part 2 
 
3.5.3.3 Calculation of the shear capacity in the region cracked in bending 
The design value of shear capacity in a region which in the ultimate limit state is cracked in 
bending, is calculated according to equations (6.2.a) and (6.2.b) of Eurocode 2 [3]: 
 
 𝑉𝑉𝑅𝑅𝑅𝑅,𝑐𝑐,𝑠𝑠𝑠𝑠 = �𝐶𝐶𝑅𝑅𝑅𝑅,𝑐𝑐 ∙ 𝑘𝑘 ∙ (100 ∙ 𝜌𝜌1 ∙ 𝑓𝑓𝑐𝑐𝑐𝑐)1 3⁄ + 𝑘𝑘1 ∙ 𝜎𝜎𝑐𝑐𝑠𝑠� ∙ 𝑏𝑏𝑤𝑤 ∙ 𝑑𝑑 (3-11) 
 
with a minimum of 
 
 
 𝑉𝑉𝑅𝑅𝑅𝑅,𝑐𝑐,𝑠𝑠𝑠𝑠 = �𝑣𝑣𝑐𝑐𝑖𝑖𝑛𝑛 + 𝑘𝑘1 ∙ 𝜎𝜎𝑐𝑐𝑠𝑠�𝑏𝑏𝑤𝑤 ∙ 𝑑𝑑 (3-12) 
 
where: 
fck is the characteristic concrete compressive strength 
d the effective depth of the total hollow core floor: d = h - ypt 
k = 1 + �200
𝑅𝑅
≤ 2.0 
ρl = 
𝐴𝐴𝑝𝑝
𝑏𝑏𝑤𝑤𝑤𝑤
≤ 0.02 
Task Group DRAFT 
23 
 
Ap is the area of the prestressing tendons, which for the required tendon force are fully 
anchored beyond the section considered. In regions cracked in bending the required 
tendon force shall be increased due to inclined shear cracks initiated from bending 
cracks. 
bw is the smallest width of the cross-section in the tensile area in mm 
σcp is the concrete compressive stress at the centroidal axis due to axial loading 
and prestressing (NEd > 0 in compression) 
 = NEd/Ac < 0.2 fcd , expressed in N/mm² 
NEd is the axial force in the cross-section due to loading or prestressing expressed in N 
(NEd > 0 for compression). 
Ac is the area of concrete cross section in mm² 
VRd,c,sf is the design value of shear flexure capacity in N 
 
The recommended values of CRd,c , vmin and k1 according to Eurocode 2 [3] are: 
 𝐶𝐶𝑅𝑅𝑅𝑅,𝑐𝑐 = 0.18 𝛾𝛾𝑐𝑐⁄ 
 𝑣𝑣𝑐𝑐𝑖𝑖𝑛𝑛 = 0.035 ∙ 𝑘𝑘3 2⁄ ∙ �𝑓𝑓𝑐𝑐𝑐𝑐 
 𝑘𝑘1 = 0.15 
 
where: 
γc is the partial safety factor for concrete, 
 
A calculation example is given in fib Bulletin xx, Part 2. 
 
 
Task Group DRAFT 
24 
3.5.4Shear-bending interaction 
The design of a hollow core cross-section with respect to shear and flexure can be carried 
out on two levels of accuracy: 
3.5.4.1 Approximate analysis 
1. Calculation of the maximum shear tension capacity VRd,c,sf in the support region 
assuming a constant distributed load near to the support (bearing capacity for shear 
tension failure); 
2. Calculation of the shear flexure capacity VRd,c,st for sections cracked in bending; 
3. Calculation of the maximum bending capacity MRd in the region where the tendons 
are fully anchored for the actual tendon strength. 
 
3.5.4.2 Detailed analysis 
The bending capacity and the shear capacity is checked at all critical points in the region 
cracked in bending for the given value of the design load in ULS. 
The bending moment at a specific position x needs to be increased due to the inclined shear 
flexure crack. With the design value for shear force Vd(x) and the design value for bending 
moment Mx,d at the position x the increased bending moment Mdi(x) for the same position is 
calculated as: 
 𝑀𝑀𝑅𝑅𝑖𝑖(x) = 𝑀𝑀𝑅𝑅(x) + 1.35 ∙ 𝑉𝑉𝑅𝑅(x) ≤ 𝑀𝑀𝐸𝐸,𝑅𝑅�𝑙𝑙𝑒𝑒𝑠𝑠𝑠𝑠 2⁄ � (3-13) 
 
Where shear and bending are analyzed at the same position along the span, they cannot be 
utilized at their respective maximum capacities. For each position in the region cracked in 
bending, the combination of both should be calculated according to the following interaction 
formula. 
 
𝜂𝜂𝑀𝑀𝑀𝑀 = ��
𝑉𝑉𝐸𝐸𝑅𝑅(𝑥𝑥)
𝑉𝑉𝑅𝑅𝑅𝑅,𝑐𝑐,sf
�
4
+ �
𝑀𝑀𝐸𝐸𝑅𝑅(𝑥𝑥)
𝑀𝑀𝑅𝑅𝑅𝑅
�
4
�
1
4
≤ 1 (3-14) 
 
where ηMV expresses the utilization level for the interaction between bending moment and 
shear flexure. 
Task Group DRAFT 
25 
 
 
 
 
 
Figure 3-10 and Figure 3-11 present respectively the shear force and bending moment 
distribution from support to mid-span. The figures also indicate the capacities for shear 
tension, shear flexure and bending moment, including the reduced capacity due to limited 
anchorage capacity of the tendons close to the support. 
Using the interaction formula as suggested above results in a reduction only in the situations 
where the utilization both in shear flexure and bending simultaneously is rather high. 
 
3.5.5 Shear capacity of elements subjected to torsion 
3.5.5.1 General 
Torsion may appear at floor corners where the element is supported along its longitudinal 
edge, or in floors with large openings, skew floor supports, cantilevering slabs, etc. 
The torsional resistance may be calculated according to the classical principles and formulas. 
The area of the resisting section comprises the upper and lower flanges and the outermost 
webs of the units. During a European research project on shear and torsion in Hollow core 
slabs “Holcotors” [47], it was stated that the two outermost webs contribute to the 
resistance, except in deeper units (e.g. 400 mm) containing four or five cores where only the 
outer webs contribute. 
Figure 3-11: Acting shear force versus shear resistance 
Figure 3-10: Acting bending moment versus moment resistance 
Task Group DRAFT 
26 
The tensile stresses due to shear near the support are added to the tensile stresses arising 
from torsion. For hollow core floors with moderate uniformly distributed loading, as for 
example in residential and administrative buildings, shear alone or shear and torsion is usually 
not governing. 
A specific torsion situation, which is not always recognized by designers, happens with an 
asymmetric position of the supporting beams as shown in Figure 3.9-1(a). The position of the 
edge columns of the first bay is shifted with respect to the columns of the central row. Floor 
units near to a column are especially subjected to torsion due to differential deflection of the 
supporting beams. In the past, in some projects, a longitudinal crack was observed over the 
whole length of a single unit. Although such a crack normally does not seriously affect the 
load bearing capacity, this situation should be avoided. 
Hollow core units are also susceptible to cross-diagonal deformation, due to end supports 
being tilted in opposite directions, which is the most likely cause of torsion cracking in Figure 
3-12. 
 
Figure 3-12: Examples of locations in precast floors where torsion may appear 
 
3.5.5.2 Torsional moments in hollow core floors 
Torsion is induced into a hollow core unit due to eccentric loads from trimmer angles at 
voids or linear line loads or point loads acting at the edges of the units which cannot be 
transversely distributed into the slab field according to the theories in Section 4.5 because of 
the presence of large voids in the floor as shown in Figure 3-13. 
Task Group DRAFT 
27 
 
 
Figure 3-13: Example of torsion induced into unit A from trimmer angles at B. After the longitudinal joint C is 
concreted the remainder of the floor loads pass through the joint. A wall built around the void at D also imposes 
a load at point B. The trimmer and wall loads imposed in unit E are distributed across the slab field to the right 
in the photograph. 
 
3.5.5.3 Torsional stiffness and strength of solid and hollow core unit sections 
For a rectangular or circular cross-section subjected to a torsional moment T, the rotation 
gradient dφ/dx of the cross-section is defined by the torsional rigidity C by the equation: 
 
 𝑑𝑑𝑑𝑑
𝑑𝑑𝑥𝑥
=
𝑇𝑇
𝐶𝐶
=
𝑇𝑇
𝐺𝐺 ∙ 𝐾𝐾𝑇𝑇
 (3-15) 
 
where: 
T is the torsional moment 
φ is the rotation angle 
C is the torsional rigidity G·KT 
G is the shear modulus: G = E / (2· (1 + v)) 
ν is Poisson’s ratio taken as 0.2 
KT is the cross-sectional factor for torsional rigidity. For a circular section it is the 
same as the second area of moment along the polar central axis. 
 
For a solid rectangular cross-section of width b larger than the depth h the cross-sectional 
factor is: 
Task Group DRAFT 
28 
 
 
𝐾𝐾𝑇𝑇,𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑅𝑅 =
𝑏𝑏ℎ3
3
�1 − 0.63
ℎ
𝑏𝑏
� (3-16) 
 
The shear stress in a cross-section subjected to pure torsion (Saint-Venant torsion) can be 
calculated as: 
 
 
𝜏𝜏𝑇𝑇 =
𝑇𝑇
𝑊𝑊𝑇𝑇
 (3-17) 
 
where WT is the torsional modulus of the section (m3) 
The shear stress due to torsion is largest at the outer surface of a solid rectangular section. 
The largest shear stress is at the midpoint of the wider surfaces. For thin walled tubular cross-
sections, the shear flow in the walls is constant and the largest shear stress is in the wall with 
minimum thickness. For a hollow core cross-section, the torsional stiffness and resistance is 
very similar to a tubular thin walled box section as idealized in Figure 3-14. It is recommended 
not to take account of the potential contribution of the longitudinal joint between the units 
in the torsional resistance. The interaction is uncertain because of possible shrinkage cracks 
in the joint, and the contribution will in any case be small since the exterior web will 
participate in the first place. 
 
Figure 3-14: Transformation of a hollow core cross-section into a tubular cross-section for calculation of 
torsional cross-sectional properties. In the present example, the longitudinal joints are not considered. 
For a thin walled rectangular cross-section shown in Figure 3-14 the cross-sectional factor is: 
Task Group DRAFT 
29 
 
 
𝐾𝐾𝑇𝑇 =
4 ∙ 𝐴𝐴𝑇𝑇2
∑𝑢𝑢𝑖𝑖𝑡𝑡𝑖𝑖
 (3-18) 
 
where 
AT is the torsional core area (shaded area in Figure 3-15) 
 = �𝑏𝑏𝑏𝑏 − 𝑏𝑏𝑤𝑤,𝑠𝑠𝑜𝑜𝑐𝑐� ∙ �ℎ −
ℎ𝑓𝑓,𝑡𝑡𝑡𝑡𝑝𝑝+ℎ𝑓𝑓,𝑏𝑏𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏
2
� 
bb is the width of the idealized box section, equal to the width of the hollow core 
element at mid-height 
bw,out is the width of the outerweb at mid-height 
ui is the perimeter of the cross-section 
ti is the wall thickness 
∑ ui /ti =
𝑏𝑏𝑏𝑏−𝑏𝑏𝑤𝑤,𝑡𝑡𝑜𝑜𝑡𝑡
𝑐𝑐𝑡𝑡𝑡𝑡𝑝𝑝
+ 𝑏𝑏𝑏𝑏−𝑏𝑏𝑤𝑤,𝑡𝑡𝑜𝑜𝑡𝑡
𝑐𝑐𝑏𝑏𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏
+ 2 ∙
ℎ−
ℎ𝑓𝑓,𝑡𝑡𝑡𝑡𝑝𝑝+ℎ𝑓𝑓,𝑏𝑏𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏