Experimental and Numerical Assessment of the Service Behaviour of an Innovative Long-Span Precast Roof Element
International Journal of Concrete Structures and Materials
Experimental and Numerical Assessment of the Service Behaviour of an Innovative Long-Span Precast Roof Element
Bruno Dal Lago 0
0 Department of Civil and Environmental Engineering, Politecnico di Milano , P.za Leonardo da Vinci, 32, 20133 Milan , Italy
The control of the deformative behaviour of pre-stressed concrete roof elements for a satisfactory service performance is a main issue of their structural design. Slender light-weight wing-shaped roof elements, typical of the European heritage, are particularly sensitive to this problem. The paper presents the results of deformation measurements during storage and of both torsional-flexural and purely flexural load tests carried out on a full-scale 40.5 m long innovative wing-shaped roof element. An element-based simplified integral procedure that de-couples the evolution of the deflection profile with the progressive shortening of the beam is adopted to catch the experimental visco-elastic behaviour of the element and the predictions are compared with normative close-form solutions. A linear 3D fem model is developed to investigate the torsional-flexural behaviour of the member. A mechanical non-linear beam model is used to predict the purely flexural behaviour of the roof member in the pre- and postcracking phases and to validate the loss prediction of the adopted procedure. Both experimental and numerical results highlight that the adopted analysis method is viable and sound for an accurate simulation of the service behaviour of precast roof elements.
precast concrete; pre-stressing; roof elements; non-linear modelling; visco-elasticity; full-scale experimentation
The prediction of the deformative behaviour of a
prestressed member is in general a challenging design task, due
to the combination of several interacting phenomena, among
which the conditions of hardening, the relaxation of steel,
the creep and the shrinkage of concrete. Wing-shaped
precast roof elements used in industrial buildings (Fig. 1) are
particularly sensitive to this issue, due to their typical high
slenderness associated with lightness.
This issue has been a fascinating research subject with
direct field application since the diffusion of pre-stressed
concrete and keeps attracting the interest of researchers. A
comprehensive overview of the problem is available in Dal
Lago (1973) with specific reference to pre-stressed members
and in CEB (1984). Martin (1977) introduced the multiplier
method for the estimation of long-term camber/deflection in
the version most commonly used in normative approaches.
More recently, Barr and Angomas (2010) analysed the
camber of bridge deck members and compared it with
different analytical and numerical methods of estimation,
attributing the differences mainly to the effect of
temperature. Roller et al. (2011) found an over-estimation of the
camber values in time by analysing a bridge member with
reference to the American standards. A comparison between
experimental deflection and numerical prediction was also
performed in Tadros et al. (2011). Breccolotti and Materazzi
(2015) performed experimental testing on the deformative
behaviour in storage of a widely diffused wing-shaped roof
element. The influence of the curing process and thermal
history during early stage hardening was described in Roller
et al. (2003), Storm et al. (2013) and Lee et al. (2016a, b).
Fig. 1 Industrial building with wing-shaped roof elements.
Rosa et al. (2007) calibrated a visco-elastic model on the
basis of a series of field measurements of the camber
evolution in bridge girders. A fully coupled sectional-based
mechanical model was presented in Pisani (2012) and
applied to a case study in Bamonte and Pisani (2015).
The European approach contained in EN 1992-1-1:2005
(2005) (Eurocode 2) is used as a reference. The standards
Model Code 2010 (CEB-FIB 2013) and ACI 318 (ACI
2008) provide alternative approaches. Gribniak et al. (2013)
provided a comparison among the different standard
approaches, stating that Eurocode 2 is usually on the safe
side, which means that the predicted long-term deflection
values for R.C. beams are higher than the observed.
However, for a correct service design of a pre-stressed R.C.
beam, the prediction of a higher camber value falls on the
unsafe side. Singh et al. (2013) made a comparison of the
effect of the different models proposed for concrete
hardening on the evaluation of pre-stressing losses of a bridge
Recent research activity specifically devoted to precast
structures performed at European level mainly focused on
the seismic performances of the structure and the
connections (Biondini and Toniolo 2010; Toniolo 2012; Biondini
et al. 2013; Colombo et al. 2014; Belleri et al. 2014; Dal
Lago et al. 2016b; Ercolino et al. 2016), but also innovative
materials attracted growing attention (Crossett et al. 2015;
Dal Lago et al. 2016c). The latter subject requires a new
definition of the main parameters used for the prediction of
the long-term behaviour of the member, or the introduction
of explicit mechanical approaches, as suggested by Bischoff
(2005) and Knight et al. (2015).
Several authors investigated the behaviour up to failure of
wing-shaped precast elements with sophisticated models
combining mechanical and geometric non-linearities
(Belletti 2009; di Prisco et al. 2012; Belletti et al. 2016) and
through experimental testing (Carbonari et al. 2013). Static
tests on full-scale precast beams of exceptional length were
carried out by Kim et al. (2016).
2. Wing-Shaped Precast Roof Element Under
The service behaviour of an innovative long-span roof
element part of a precast system for industrial buildings
(Ondal , Fig. 2) is studied both experimentally and
numerically in this paper. This roofing typology is
representative of an important portion of the European heritage of
industrial buildings since the late 80s (Dal Lago and
Mantegazza 1988) up to today. The novel element has a
lightweight Y-shaped cross-section with a depth of 1.5 m and a
width of 2.5 m with a hollow core positioned at the bottom,
which increases the torsional stiffness and resistance with
respect to the typical V shape of the shallower standard
element of this system (Breccolotti and Materazzi 2015).
The edges of the element are shaped for the connection with
the beam. The novel element was engineered to cover spans
up to 42 m.
Fig. 2 Components of the Ondal system for industrial buildings (courtesy of DLC consulting).
An element spanning 40.5 m was subjected to monitoring
in storage and experimental testing. Figure 3 shows the
cross-section of the case study element. It was reinforced
with 21 d15.2 main tendons and 6 d12.5 secondary tendons
made of fp(0.1)k 1860 pre-stressing steel, all pre-stressed at
1400 MPa. Plastic debonding sleeves were applied to
selected main strands in order to limit the concrete tension
close to the element ends. Grade B450C Mild steel rebars
and grade B450A nets were also added. Table 1 lists the
longitudinal reinforcement of the element. The transversal
reinforcement was made of two welded wire meshes
running around the core, for a total of 157 mm2 every
200 mm. Eight U-shaped d12 transversal bars were added
at each end with spacing of 38 mm. The concrete used was
declared by the producer to be of class C50/60, but
crushing tests performed at 28 days by the producer on
cubic concrete specimens showed that the actual class was
between C55/67 and C60/75. Table 2 contains the main
mechanical properties of the materials that were used.
The element was cast in special self-reacting metallic
formworks (Fig. 4) made by a fixed bottom mould and a
rotating counter-mould with hydraulic opening system (Dal
Lago et al. 2016a). The formwork is provided with vibration
and heating systems for the accelerated hardening of SCC.
The pre-stressing system is hydraulic with the use of
prestressing tendons linked to the pulling system through steel
Figure 5 shows pictures of an industrial building using
the roof element under investigation in phase of
3. Behaviour in Storage
The check of camber and shortening of pre-stressed
manufacts in the phase of storage is an important practice for
the quality check of the product and an important potential
alarm of design or technological problems.
Fig. 3 Wing-shaped precast roof element under investigation.
Table 1 Longitudinal reinforcement of the case study roof element.
De-bonding sleeve length
from ends (mm)
Table 2 Material properties.
3.1 Theoretical Background
A time-step procedure was implemented for the correct
estimation of the deformative behaviour of pre-stressed
elements in visco-elastic range. The procedure is based on
the time-step evaluation of the visco-elastic phenomena
linked to the member longitudinal shortening and its
subsequent deflection profile. The geometrical
non-linearity of the problem displays due to the following
The pre-stressing reinforcement generates a constantly
distributed moment distribution which is linearly
depending on the stress of the strands and, if properly
designed, leads to an upward deflection profile in service
with camber at mid-span, subjected to a visco-elastic
behaviour in time: v = f(rp,u).
A longitudinal visco-elastic shortening of the member
due to the axial load induced by the pre-stressing leads to
elastic losses in the strands, whose axial stress is lowered
after shortening: rp = f(u).
Since the deflection profile of the member depends on
both longitudinal deformation and deflection profiles,
both visco-elastically evolving, the two are coupled:
v = f[rp(u),u].
Furthermore, the viscous axial shortening of pre-stressed
elements is particularly relevant, since they are subjected to
strong axial loads applied in an early stage of concrete
hardening due to the daily schedule typical of the industrial
With reference to the behaviour in storage of pre-stressed
elements, the elastic contribution always has a monotonic
decreasing tendency, due to the combination of the following
visco-elastic shortening of the element and subsequent
elastic losses in the bars,
relaxation of the pre-stressing reinforcement,
shrinkage of concrete,
while the creep contribution, if the elastic component is
always positive, is also always positive with a monotonic
increasing trend. The combination of those terms determines
the overall deformation behaviour of the element, which
could also be subjected to trend reversal of the deflection in
Fig. 4 Particular view of the end of the mould with mild and
pre-stressing steel reinforcement ready for casting.
Fig. 5 Assemblage of a precast industrial building with the
case study roof element (courtesy of Angelo Basso):
aerial view (a), internal view (b).
the range of downwards values, difficultly predictable
without an accurate evaluation of the element shortening
evolution in time.
The employed methodology solves the problem by means
of semi-analytical techniques through a discretisation in the
time domain, under the hypotheses of plane sectional strain
profile and homogeneous section. In particular, the
longitudinal behaviour of the element and its deflection
profile are considered as uncoupled, and the formulation is
corrected with linear terms in order to take into account in a
simplified way the real coupling. As a consequence of such
an hypothesis, it is possible to formulate the longitudinal
shortening first, and subsequently compute the deflection
history as a function of the shortening tendency.
The deflection profile of a member is calculated in
accordance with the well-known visco-elastic model having
the integral form of Eq. (1) (see Branson 1977; Migliacci
and Mola 1985, Mola 1997; Ghali et al. 2011; Mola and
where the visco-elastic deflection v at time t is expressed as
the sum of a contribution of the elastic deformation
computed at time t to which the contribution of creep,
depending on the first derivative of the creep coefficient
u(t,t0), has to be summed. A similar equation defines the
visco-elastic longitudinal strain equation for pre-stressed
members with constant cross-section [Eq. (2)], depending
on the elastic [Eq. (3)], creep [Eq. (4)] and shrinkage
elong ðt; t0Þ ¼ eelðt; t0Þ þ ecreepðt; t0Þ þ ecsðtÞ
where the mean stress in the pre-stressing reinforcement can
be defined as per Eq. (5), taking into account the relaxation,
thermal and shortening losses:
where an anchorage factor uanch is simply defined in average
terms for the distribution of debonding sleeves and
anchorage of the cables [Eq. (6)]:
and uv is a weighted factor for curvature loss taking into
account the combination of parabolic-shaped deformation
profile due to pre-stressing and fourth order polynomial
function deformation profile due to distributed loads
(selfweight), to which the maximum bending moments M’ e M*,
respectively, belong [Eq. (7)]. The uv factor is always lower
The non-linearity of Eq. (2) is clear, due to the presence of
the unknown elong in the integral belonging to the creep term.
The solution is not achievable in closed form, and the
equation needs to be solved with the aid of numerical
It is though possible to identify an approximated solution
with independent variables estimating the loss for shortening
of the member, through a fictitious stiffening of the axial
By eliminating the unknown from the formulation of rp
and by making its contribution explicit in the equation of the
elastic deformation eel, the latter can be written as follows
eelðt; t0Þ½1 þ /ðt; t0Þ EpAp
By operating the proper simplifications, it is then possible to
define the elastic deformation term eel as per Eq. (10):
defining the equivalent axial stiffness EAeq as follows
EAeqðt; t0Þ ¼ EcmjðtÞAc þ EpAp½1 þ /ðt; t0Þ
In this way, the integral equation is fully explicit and can be
solved without the need of iteration.
The deformation of the case study element during its
storage phase was monitored with low precision instruments
(rolling tape for shortening and analogue deflection gauge
for mid-span deflection), typical of the standard control of
production, having as objective a global check. Figure 6
reports the measures.
The above-described numerical procedure was applied to
the roof element under investigation. In order to make its
solution comparable with the simplified formulation of EN
1992-1-1:2005 (2005) (Eurocode 2), all data related to
timedependent properties of materials was taken from that
standard. The numerical curves related to the evolution in time
of axial shortening and mid-span deflection are reported in
Fig. 6 in comparison with the experimental measurements.
The axial behaviour is well predicted by the numerical
algorithm, and the deflection shows a tendency to stabilise
on a plateau, in accordance with the experimental data, but
Fig. 6 Numerical prediction of mid-span camber and
shortening time history compared with experimental
on a slightly over-estimated value. It can be observed that
the difference between the numerical and experimental
plateau value of the mid-span camber, of about 14 mm, is
limited to only 1/3000 of the span.
EN 1992-1-1:2005 (2005) part 1-1 provides a closed
formulation for the calculation of elastic and time-dependant
losses in accordance with the multiplier method, reported in
ecsEp þ 0; 8Drpr þ EEcpm /ðt; t0Þrc;Qp
The prediction of the evolution in time of the deformation
calculated in accordance with this simplified criterion leads
to a curve that is sensibly different from that obtained with
the proposed formulation, with a relevant under-estimation
of the mean pre-stressing losses, to which a larger camber of
the element in time is associated. Figure 7 shows the
comparison of the two loss curves plotted with a logarithmic
function of the time. At the day of execution of the tests,
14 days from casting, the mean pre-stressing loss estimated
through the time-step proposed formulation is equal to
15.0%, while the simplified formulation leads to 11.7% of
proposed formula on
EC2 simplified formula on
Fig. 7 Evolution of pre-stressing losses in time: comparison
of the adopted explicit integral formulation and the
simplified formulation of EC2.
4. Load Tests and Numerical Simulations
4.1 Test Setup
The roof element monitored in storage was later subjected
to load testing at the Antonio Basso company production
plant in Treviso, Italy. Two loading tests were carried out in
order to verify the mechanical behaviour of the element
under combined flexure and torsion in elastic field and under
pure flexure in pre- and post-cracking fields. Figure 8 shows
sketches of the loading apparatus and of the measurement
setup. Pictures of the experimental setup are shown in
Figs. 9 and 10 shows particular views of the
instrumentation. 30 hydraulic jacks were used in parallel to apply a
quasi-uniformly distributed load to the element. They have
been positioned along ten sections distanced by 3.70 m and
connected at each section at both wing edges and at the
centre. Repartition steel beams were placed at the edges to
better distribute the load. The jacks were connected with
bundles of rebars placed underneath the element, used as
counter-acting weight, having an approximated global mass
equal to 60 tons. One vertical displacement transducer was
positioned in correspondence of each of the jacks positioned
at the quarters of the span, for a total of nine vertical LVDTs,
with three additional horizontal transducers placed at the top
of the element at the quarters of the span with the aim to
measure the relative opening of the wings. The vertical
displacements are subtracted to the small deformation of the
element in correspondence of the supports, measured by two
vertical LVDTs with short stroke. The load tests were carried
out by 4EMME (Altinier 2015).
4.2 Combined Flexure–Torsion Test
The first test carried out was the one of combined flexure
and torsion, where the load was applied to one row of jacks
placed in correspondence of one wing only. In such a way,
the vertical load was applied with an eccentricity equal to
half of the width of the element with respect to its centre of
the mass. The test is aimed at simulating the positioning of
the structural completing shells on top of the roof element
(Fig. 2), which is typically performed one span per time,
studying the stability of the element under this temporary
Under an equivalent distributed load of 1.66 kN/m, a
maximum torsional rotation of 0.23 rad was measured at
mid-span, together with a wing distancing limited to half a
millimetre in the same section. This shows the efficiency of
the full collaboration of the cross-section. A computer model
using 8-node hexahedra brick elastic elements (32 elements
were used to describe the cross-section, each 250 mm long,
for a total of 5248 brick elements) was developed with
Straus7 (G?D Computing 2010) for the simulation of the
test. The end shaping of the element provides a torsional
Fig. 8 Test setup: positioning of loading apparatus (a) and instrumentation (b).
clamp at the element ends, which in real constructions is also
enhanced by distanced dowels, not used in the load test. The
deformation profile of the mid-span cross-section of the
beam torsionally clamped at the supports is shown in
Fig. 11. Using an elastic modulus equal to 37 GPa, which
was obtained from the elastic modulus growth curve in time
provided by EC2 for a concrete in between classes C55/67
and C60/75 at 14 days, the numerical simulation provides
vertical displacements equal to 12-17-21 mm in the
monitored points. This displacement profile yields to a torsional
rotation angle of 0.21 rad, which is close to the measured
4.3 Flexure test
The flexure test has been carried out by applying the same
oil pressure to all hydraulic jacks. The graph of Fig. 12
shows the experimental equivalent distributed load versus
mean mid-span deflection calculated as the average of the
three measurements taken at wings and centre. Two load
cycles were performed.
After an elastic branch in which all sections of the element
were fully compressed, cracking was attained at about 10 N/
mm, after which the experimental curve shows a softening
tendency due to the diffusion of cracking from mid-span
towards the supports.
A picture of the mid-span area of the element with the
flexural crack pattern post-marked with the aid of the
computer is shown in Fig. 13a. The cracks were all of modest
opening and difficult to be observed.
The test was interrupted at the attainment of an equivalent
distributed load of 14.0 N/mm (the SLS load for this element
was calculated to be 10.0 N/mm), due to the uplift of the
counter-acting strand bundles. Cracks at mid-span reached a
height of about 600 mm from the bottom (Fig. 13a). The
maximum wing opening was measured equal to 13 mm at
mid-span, corresponding to practically negligible
shallowing. The element, once the load was removed, showed
negligible residual deflection and completely closed the
cracks developed during the test, which suggests that the
strands were not plasticised.
A non-linear semi-analytical mechanical model was
implemented with the aim to compare the experimental
results. The model is based on the evaluation of the
Fig. 11 Numerical simulation of the combined flexure–torsion test: deformed shape of the mid-span cross-section.
40 60 80 100 120 140
Mean deflec on at mid-span [mm]
Fig. 12 Flexure test: distributed load versus
linear moment vs curvature diagram of the current
crosssection in pre-stressed concrete and on the later solution of
the equation of the inelastic curve. A Sargin model (Sargin
1971) was used to model concrete in compression
considering the above deduced base compressive strength
(Fig. 14a), an elastic–plastic model with parabolic plastic
branch was used for grade B450C mild steel (Fig. 14b) and
an elastic–plastic relationship with linear hardening was
used for pre-stressing steel having fp(0.1)k equal to 1860 MPa
(Fig. 14c). The strength values were not divided by safety
coefficients, in order to catch the experimental behaviour of
Figure 15a shows the non-linear moment vs curvature
diagrams of the cross-section corresponding to mean
prestressing losses equal to 0, 15 and 30% obtained through the
solution of the translational and rotational equilibria of the
section neglecting the tensile strength of concrete. It can be
observed that, as well known by the designers, the
prestressing losses do not influence neither the resistance of the
element nor its ductility, due to the plastic properties of steel.
To be noted that the analytical model developed does not
take into account possible preliminary failures due to local
instability. On the contrary, a relevant influence of the losses
is observed with respect to the cracked moment, diminishing
with higher losses, which is a fundamental parameter for a
good behaviour of the manufact in service. The expected
concrete stress distribution along the depth of the section is
reported in Fig. 13b either considering or neglecting the
tensile strength of concrete. A better correspondence with
the height attained by the cracks observed on the element is
obtained considering the tensile strength of concrete. It can
be observed that the expected crack moment Mcrack of the
section with mean losses of 15%, as estimated in the
previous paragraph after 14 days of ageing, is equal to about
4000 kNm. The uniformly distributed load corresponding to
first cracking at mid-span is equal to qcrack = 8Mcrack/
L2 = 19.5 N/mm. In the experimental curve obtained with
the flexure test an inflection point corresponding to cracking
initiation is observed for a load of about 10 N/mm (Fig. 12).
By subtracting to the total load the structural self-weight,
equal to 10.0 N/mm, which is already acting before the test,
the crack load is estimated with good precision. This
confirms the estimation of about 15% of losses, providing a
validation of the results of the time-step numerical procedure
The numerical prediction matches with good precision the
experimental curve corresponding to the second cycle,
slightly underestimating the cracked stiffness of the first
cycle which is larger due to the contribution of the tensile
strength of concrete, not anymore playing a role in the
second cycle. The obtained non-linear moment vs curvature
diagram is used to get the deflection profile of the element by
solving the inelastic curve formula v’’ = h(M) governed by
a 2nd order differential equation. Figure 15b shows the
numerical deflection profile corresponding to the application
with tensile strength
w/out tensile strength
Fig. 14 Non-linear material properties for: concrete (a), mild steel (b) and pre-stressing steel (c).
of 24 N/mm, equal to the sum of the structural weight load
and the maximum equivalent distributed load given by the
jacks, depurated by the pre-camber. The experimental points
included in the graph show that the estimation is sound.
The service behaviour of an innovative wing-shaped
precast roof element was experimentally investigated by means
of deformation monitoring during its storage phase and of
both torsional–flexural and purely flexural load tests. The
results of the load tests show that the element, even if
characterised by a relevant slenderness, is scarcely subjected
to cross-section distortion under both loading conditions.
An element-based mechanical formulation was
implemented to predict the visco-elastic behaviour of pre-stressed
concrete members with constant cross-section. It is based on
a time-step integral formulation explicitly taking into account
the coupling of creep and shrinkage of concrete and
relaxation of steel for the determination of pre-stressing losses and
both axial deformation and deflection profiles over time. The
application of this model to the case study brings to a sound
estimation of the experimental deformation profiles. The
results of the linear 3D fem model used to investigate the
torsional–flexural behaviour of the element are also in good
agreement with the experimental observation. The non-linear
mechanical model used for the estimation of the crack load
and the deflection profile of the beam in post-cracking phase
is able to catch the experimental measurements and provides
further confirmation of the validity of the formulation
adopted for the estimation of pre-stressing losses over time
and the subsequent deflection profile.
The non-negligible scatter between the losses in time
predicted with the proposed formulation and the simplified
one provided by Eurocode 2 based on the close-form
multiplier method suggests that further studies should be carried
out in this field.
DLC Consulting of Milan, Italy, is acknowledged for the
design and engineering of the roof member studied in the
paper, in particular Alberto Dal Lago and Uberto Marchetti.
The production of the member subjected to testing and the
assemblage of the first buildings made with the system were
carried out by Antonio Basso precast company of Treviso,
Italy. Special thanks go to Angelo Basso for his deep interest
in the development of the work. Dr Francesco Foti from
Politecnico di Milano is acknowledged for his contribution
in the definition of the visco-elastic semi-analytical model.
Dr. Patrick Bamonte from Politecnico di Milano is also
acknowledged for his suggestions. Finally, the testing
company 4EMME of Treviso, Italy, is acknowledged for
the execution of the experimental load tests.
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