Size effect on long term deflection of RC and PC bridges

Concrete Laboratory
Menchaca Sosa Arturo Alejandro
Professor Shimomura Takumi

1. Introduction.
At design stage, concrete structures must be designed
following a strength criterion, whose are generally extrapolated
to sizes that are often much larger than a structural size that canbe tested in the laboratory, to guarantee its safe structural life.
Until now, most of the studies in the matter of size effect werefocused on assessments of failure strength of concrete. On theother hand, previous works that treated about long-term
deflection phenomena only discussed its impact on thestructural durability. However, previous studies have neverdiscussed about size effect on long-term deflection, which
implies that to nonlinear analysis is the only mean to implicitly
evaluate it and there is no a basis data to explain whether or not
this behavior affects the structural safety.
This works aims to clarify the nonlinear characteristics of size
effect on long-term deflection behavior. Hence, the dominantfactors on the variation of size effect in time-dependent
deflection will be discussed, through numerical simulations.
Moreover, the difference of size effect on long-term deflection
in comparison with shear strength criteria will be investigated tounderstand its importance on safety structural designs.
2. Experimental Study.
2.1 Specimen details and exposure-loading test
As a starting point, an exposure loading-test was conducted toverify the long-term deflection characteristics of concrete
member with different volume-surface ratio.
RC and PC slabs with 100 mm (height)×300 mm (width)×3900 mm(length) of geometry, were adopted for this experiment,
as it is illustrated in Fig. 1abcde to observe the difference oftime-dependent deflection through variation of superficial
drying-swelling (volume-surface ratio), at two categories ofconcrete structures. RC & PC slabs and prismatic specimens
were installed during winter, at campus of Nagaoka Universityof Technology, where exposure began by November 4th, 2017.
The test setting was carried out following the diagram of Fig.
1a. The deflection was measured by displacement meters,
located in 3 positions at bottom surface of the slab. Theenvironmental conditions were monitored, utilizing a weather
station located near of specimen set, at intervals of one hour.
Currently, the present exposure-loading test is still going on,
gathering measurements.

(b)

RC-W

Epoxy
Resin
Layer

Concrete

(a)
(c)

RC-S

(d)

PC-W

(e)

PC-S

Epoxy
Resin
Layer

Cross-section of eachspecimen.

Fig. 1: Specimen seal conditions andexposure-loading test layout.

Fig. 2: Comparison of analytical results andexperimental data of RC slabs deflections.

2.2 Results & discussion.
Measurements results were summarized for 360 days ofexposure. The results of deflections at mid span of RC and PC
slabs are plotted as dotted lines, in Fig. 2 and Fig. 3, respectively.
Observing these, the increase of time-dependent deflection with
the increasing of surfaces exposed to sunlight and rain, on RC
slabs as well as PC slabs, was confirmed.
Therefore, based on experimental observations, it wasconcluded that the rate of long-term deformation is affected by
the number of surfaces exposed to sunlight and rain.
3. Numerical verification.
Numerical analysis of this study was performed discretizing
the slabs into portions where through moisture transport as well
as stress-strain analysis was carried out to compute the curvatureand deflections of at mid span of the slab. Numericalcomputations of time dependent deflections of RC and PC slab

Fig. 3: Comparison of analytical results andexperimental data of PC slabs deflections.

were plotted as solid lines of Fig. 2 and Fig. 3, respectively.
Observing these results, it was confirmed that computation
models can describe the tendency of time-dependent deflectionof each specimen, considering shrinkage distribution at crosssection, creep, its sealing conditions as well as environment
conditions.
4. Study of size effect on long-term deflection
Size effect on long-term deflection was investigated throughnumerical simulations, varying structural sizes on two different
shapes: Prismatic girder and Box Girder.
The computations were conducted on 50 years of exposure
period by considering structural self-weight as dead loads.
Calculations results of relative values of time-dependent
deflection were plotted on Fig. 4 and Fig. 5. Observing theseresults, the decreasing of ambient actions on time-dependent
deflection when member size increase, was confirmed.
Furthermore, was observed that fluctuations of time-dependent
deflection decreases with the increasing of structural size.
Moreover, deflections at 50th year of member exposure weresummarized against to member size, as its exhibited on Fig. 6and Fig. 7. Through these results, its remarkable to concluded
that the nonlinearity of size effect on long-term deflection wasclarified.
5. Conclusions
This research was focused to study the nonlinear
characteristics of size effect on long-term deflection behavior, tounderstand its importance on structural design, as it isconsidered in failure strength criteria. Following this basis,experimental and analytical studies of exposure-loading test
were carried out and, the earned remarks were summarized asfollows:
1. Numerical models that were developed for hygrothermal
analysis, were couple with stress-strain models to predict
long-term deflection and these were verified by acomparison of experimental data of exposure tests.
2. Long-term deflection characteristics were observed andsummarized through considerations of surface-volume
ratio of concrete member.
3. Size effect on long-term deflection was clarified throughnumerical simulations. The obtained results demonstrated
the decreasing of ambient action effects on long-term
deflection as the structure size increases. Also, fluctuationsof time-dependent deflection decreases when structuralsize increase.
In other words, remarks from above does implies that sizes
effect on long-term deflection reduce the risk of serviceability
from long-term deflection.

𝛿 𝑡𝑖𝑚𝑒 : time dependent
deflection
𝛿 𝑡 : instantaneous
deflection

Fig. 4: Relative values of time-dependent
deflections of PC prismatic girders.

Fig. 5: Relative values of time-dependent
deflections of PC box girders.

Fig. 6: Size effect of time-dependent
deflections of PC prismatic girders.

References.
[1] Zdenek P. Bazant and Jin-Keun Kim, Size effect in shear
failure of longitudinally reinforced beams, ACI Journal
81-38, 1984, pp. 456-468.
[2] Toru Shiga, Tetsuo Abe, Masataka Watanabe, Takumi
Shimomura, 2016, Influence of environment on long-term
deflection of RC and PC beams exposed to ambientconditions, Proceedings of the Japan Concrete Institute,Vol.38, No.1, pp. 483-488．
[3] T. Shimomura and K. Maekawa, 1997, Analysis of
the drying shrinkage behavior of concrete using a
micromechanical model based on the micropore structureof concrete, Magazine of Concrete Research, 49, No. 181.
Fig. 7: Size effect of time-dependent
deflections of PC box girders.
deflections.