Computation of Post-Tensioned Slab Deflection under Construction Loads

Ah Sir Cho1, Thomas Kang2, Keenam Jeong3, Yeong Wook Jo4, and Byong Kap Jeon5

1) Ph.D. Student, Department of Architecture and Architectural Engineering, Seoul National University, Seoul, Korea.
Email: pgulmark@snu.ac.kr
2) Associate Professor, Department of Architecture and Architectural Engineering, Seoul National University, Seoul, Korea.
Email: tkang@snu.ac.kr
3) Structural Engineer, Total PS Co., Ltd., Seoul, Korea. Email: jkn@totalps.co.kr
4) Structural Engineer, Engineering & Construction Group, Samsung C&T Corporation, Seoul, Korea. Email:
yeong.jo@samsung.com
5) Structural Engineer, Engineering & Construction Group, Samsung C&T Corporation, Seoul, Korea. Email:
jbk21.jeon@samsung.com

Abstract:
In this study, deflections of post-tensioned (PT) slabs of a three-dimensional office building under construction
loads were computed using a post-tensioning (PT) specialized computer program, ADAPT, and relevant theories.
Typically a total of four floors of slabs are shored during the construction. The below three floors are already cast
with concrete and partially hardened when fresh concrete is poured at the top level of these four floors. For the
below three levels, post-tensioning of 15.2 mm diameter unbonded tendons is completed. The most below floor is
subjected to largest construction load at its entire life, and may be vulnerable to severe cracking without PT. The
reduced moment of inertia and elastic modulus of early-age concrete due to cracking (if cracked even with PT)
may affect the long-term creep behavior of the floor significantly. The construction loads also include various
loads of equipment, forms, self-weight of upper floors, and stored materials, as well as balancing uplift loads by
PT. In the computer analysis, all the aforementioned conditions were considered carefully and computationally.
The floor shoring was modeled using an elastic circular column, and its elastic modulus was input with actual
values. The PT process and prestress losses due to wedge slip, friction, elastic shortening, etc. were simulated in
the computer model. The construction loading and shoring/unshoring were taken into account. Finally, the model
also reflected possible changes of the effective moment of inertia and elastic modulus at each construction step.
The developed computational procedure helped predicting the deflection histories of PT slabs.

Keywords: Deflection, computer analysis, post-tensioned slab, construction loads, shoring, cracking.

1. INTRODUCTION
Slab deflection results in a variety of cracking problems and may lead to a serious damage or durability defect of
the building if it occurs significantly in a short time. In the construction field, rearrangement or design modification
of non-structural building materials might be needed due to the excessive deflection, especially for non-structural
mechanical systems and finishing materials. With such changes, the performance cannot be made fully as planned,
and the total construction time and cost would increase. For efficient construction, it is important to predict and
control the deflections occurring during construction well. For example, the member could be designed to have a
pre-camber or the prestressing is applied to the member using tendons. Compared to conventional reinforced
concrete (RC) systems, the post-tensioning (PT) method is applied more effectively in long span structures as a
lifting-up effect is created by tendons.
Jayasinghe (2011) predicted the deformation of PT beams and slabs over time. Rodriguez-Gutierrez and
Aristizabal-Ochoa (2007) calculated the deflection of reinforced and prestressed concrete beams and compared
with previous experiments. Hirsch (2009) suggested the method of long-term deflection prediction by using linear
elastic analysis. There are several codes and researches that suggest how to calculate the deflection of slabs or
analyze with their own program. In the case of post-tensioned (PT) building, relevant studies are still lacking. In
this paper, a PT deflection analysis is performed using a commercial finite element analysis program.

2. MODELING
For the analysis of post-tensioned slab, a finite element analysis program ADAPT (ADAPT Corporation, 2015)
was used. This is the program specially optimized for multi-story post-tensioned buildings, while other similar
program such as SAFE (Computers and Structures, Inc., 2014) is capable of analyzing PT slab only for one story.
Design codes for analysis were based on the ACI 2011 (ACI, 2011) and IBC 2012 (ICC, 2012).
2.1 Concrete
The target building is an office building constructed using the PT method. The plan view is shown in Figure 1.

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This building is under actual construction. The slab was divided into 18 zones considering the column layout and
each zone was named as shown in Figure 1. To take into account shoring over three stories, four stories were
modeled. The top floor was defined as Nth floor and the floors below the top floor were labeled as N-1th, N-2th, and
N-3th floor sequentially. Properties of concrete applied to the slab and columns of each layer are shown in Table
1. The design strength of the slab concrete was 35 MPa and that of columns was 30 MPa. The time of the initial
deflection prediction was assumed to be the time immediately after pouring concrete for the Nth floor. At this time,
poured concrete has low strength but normal weight which is the same as hardened concrete. Thus, in the analysis,
the concrete strength (f’c) of the Nth slab was 1 MPa. The columns of Nth floor were assumed to have 18 MPa
because it would be partially hardened. The concrete elastic modulus (Ec) was then automatically determined by
the strength in the ADAPT program (Aalami, 2011). For all concrete members, the unit weight of 2400 kg/m3 and
creep coefficient of 2.0 were applied.

Figure 1. Slab dimension and zoning

Table 1. Material properties of shoring

Floor  (MPa) Unit Weight (kg/m3) Type  (MPa) Creep Coefficient
N 1.00 2400.00 Normal 5026 2.0
N-1 35.00 2400.00 Normal 29734 2.0
Slab
N-2 35.00 2400.00 Normal 29734 2.0
N-3 35.00 2400.00 Normal 29734 2.0
N 18.00 2400.00 Normal 21323 2.0
N-1 30.00 2400.00 Normal 27528 2.0
Column
N-2 30.00 2400.00 Normal 27528 2.0
N-3 30.00 2400.00 Normal 27528 2.0

 = concrete strength at 28 days;  = elastic modulus of concrete.

2.2 Reinforcement and Post-Tensioning

Steel reinforcing bars and PT tendons were arranged as shown in Figure 2. The tendons were banded horizontally
in one direction, centered the column, and distributed in the other principle direction. The main longitudinal re-
bar was SD400 D13 bar (diameter = 13 mm) with a specified yield strength of 400 MPa. The yield strength of re-
bars used in the field was generally larger than the specified strength; thus, a value of 460 MPa was applied in the
analysis.
For post-tensioning, 15.2 mm diameter unbonded tendons have the ultimate tensile strength of 1860 MPa were
used. In the analysis, the same ultimate tensile strength was used and the yield strength was assumed to be 1700
MPa. The modulus of elasticity was set equal to 200,000 MPa for both the reinforcement and the PT tendon.

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 (a) Reinforcement (b) PT tendon

Figure 2. Reinforcement and PT tendon arrangement drawing

2.3 Shoring

Figure 3. Shoring plan (red dot: MP, green dot: PEP & red arrow: AS)

Shores were installed over the three floors and each floor had three kinds of shores; Multiprop (MP), PERI Euro
prop (PEP), and Aluminum form support (AS). They were spread all over the slab as shown in Figure 3. Their
material properties applied in the analysis are indicated in Table 4. The MP plays a role to reduce the deflection at
the center of each slab section. The largest number of the shoring used was PEP which is designed to resist total
loads transmitted from upper stories. The AS is commonly used for supporting only the formworks, but in the
analysis it was assumed as a prop because it shores up the drop panel.
In the ADAPT analysis, the prop was modeled as an axial member with two hinge ends and circular section having
100 mm diameter, and its unit weight was calculated by dividing the weight by the assumed volume. The main
material of MP was steel while PEP and AS were made of aluminum. The elastic moduli of MP and PEP/AS of
200,000 MPa and 70,000 MPa were input in the program, respectively. The stiffness of each member was
automatically calculated according to the modulus of elasticity during the analysis.

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 Table 2. Material properties of shoring
Shoring Quantity (EA) fu Weight (kg/EA) Unit Weight (kg/m3) E Creep Coefficient
MP 68 1583.45 18.8 626.83 200,000 2.0
PEP 339 193.97 19.2 613.77 69,999 2.0
AS 204 193.97 17.9 585.04 69,999 2.0
fu = assumed strength; E = elastic modulus

2.4 Load
Load combinations shown in Table 3 were applied in the analysis. In order to consider the most basic service load,
all factors for each load were defined as 1.0. Reinforced concrete (RC) with post-tensioning has only the weight
of concrete and construction load, and the prestressing effect was accounted for as additional PT upward load.
When the concrete was poured on the Nth floor slab, all the tendons up to the floor of N minus one floor ((N–1)th
floor) were assumed to be post-tensioned. Before concrete hardens nothing can be placed on the slab, so Nth floor
slab was subjected to only the self-weight for both the RC and PT systems.

Table 3. Load combination

Floor RC PT
N 1.0 SW 1.0 SW
N–1 1.0 SW + 1.0 LL 1.0 SW + 1.0 LL + 1.0 PS
N–2 1.0 SW + 1.0 LL 1.0 SW + 1.0 LL + 1.0 PS
N–3 1.0 SW + 1.0 LL 1.0 SW + 1.0 LL + 1.0 PS
SW = self-weight; LL = live load; PS = Prestressing.

2.5 Final Model

Applying for aforementioned conditions and information, analysis models are created by using ADAPT as shown
in Figure 4.

(a) Without shoring (b) With shoring

Figure 4. Slab and shoring modeling

3. RESULTS
The analysis results on the deflection occurring in the RC and PT slabs are shown in Figure 5, with the maximum
deflection of each floor indicated in Table 4. Both RC and PT slabs showed a similar pattern in all floors. Maximum
deflection occurred in the panel of E1. Also, in the panels of E2 and E3 second and third larger deflections occurred
in order. Maximum deflections in the panels of A1 ~ A3 are larger than those of B1 ~ B3. This means that the
more deflection occurred near the perimeter of the building. At the locations of A4, B4, C4, and D4, relatively
smaller deflections were expected. One reason might be that the widths of these slabs were smaller than those of
A1, B1, C1, and D1 panels. The other reason could be that they were substantially away from the E1 panel, the
slab most vulnerable to deflection.

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 (a) RC: Nth floor (e) PT: Nth floor

(b) RC: (N–1)th floor (f) PT: (N–1)th floor

(c) RC: (N–2)th floor (g) PT: (N–2)th floor

(d) RC: (N–3)th floor (h) PT: (N–3)th floor

Figure 5. Slab deflection contour

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In the computer analysis, there was little difference in each floor deflection, unlike the anticipation that the
deflection would be the largest in the most below floor without shoring at the time of concrete pouring on Nth floor
in proportion to the magnitudes of loads. In the analysis, the deflection of Nth floor was the largest and the
deflections were slightly reduced for (N–1)th or (N–2)th floor, but it was almost the same. The almost same
deflections were likely due to the slabs linked with shores, enabling the slabs to move. The deflection of Nth slab
resulted from not only its own weight but the push-down force from the (N–1)th slab through the integrated shoring
system. Also (N–2)th and (N–3)th floors’ weights are related to the deflections of its own floor and other floors in
a similar way. Slabs of each floor were connected with the props and these shoring members acted as elastic links
so that all the members contributed to the stiffness and associated deflection in the analysis. Thus, the difference
in deflection between the floors was not considerable.
For the PT structure, the deflection was reduced significantly as compared to the RC structure. Uplift forces by
prestressing decreased the deflection. In the analysis, it can be surmised that uplift behavior of upper slab also
affected the deflections of lower slabs through the integrated props.

Table 4. Maximum deflection (Unit: mm)

Floor RC PT
N 14.6 9.32
N–1 14.4 9.05
N–2 14.3 8.92
N–3 14.4 8.94

4. CONCLUSIONS
In this paper, 4-story part of a post-tensioned concrete building was designed using the post-tensioning-specialized
finite element program, ADAPT. For comparison, the same building without post-tensioning forces was also
analyzed. Through the analysis, both reinforced and post-tensioned structures were found to have similar aspects,
which include the fact that the maximum deflection occurred at the largest slab panel, except that the maximum
deflections were 14.6 mm and 9.32 mm in RC and PT slabs, respectively. The post-tensioning effect decreases
about 37% in deflection. Unlike the common anticipation, the deflections for all four stories were similar. This
tendency was due to the connection between the shoring and the slabs in the analysis. The props were integrated
to the slab as an elastic member. The prediction method needs to be further improved. Even so, the computer
analysis takes into account the construction loads such as the accumulated upper floor weights, the post-tensioning
effect, and the shoring effect reasonably well. Additionally, the model also reflected possible changes of the
effective moment of inertia and elastic modulus at each construction step. The developed computational procedure
helped predicting the deflection histories of PT slabs during the construction.

ACKNOWLEDGMENTS
Financial support provided by Samsung C&T Corporation is acknowledged.

REFERENCES

Aalami, B. O. (2011). Technical Note: Deflection of Concrete Floor Systems for Serviceability. ADAPT
Corporation, p.38.
ACI Committee 318. (2011). ACI 318-11: Building Code Requirements for Structural Concrete and
Commentary. American Concrete Institute, p.503.
ADAPT Corporation. (2015). ADAPT 2015. Retrieved from ADAPT corporation website:
http://www.adaptsoft.com/emailer/builder_2015_first_release.html, accessed on December 8, 2015.
Computers and Structures, Inc. (2014). SAFE 2014. Retrieved from website:
http://www.csiamerica.com/products/safe, accessed on December 8, 2015.
Hirsch, J. (2009). Accurate Long-Term Deflection Prediction in Flat Slabs Using Linear Elastic Global Analysis.
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ICC. (2012). 2012 International Building Code. International Code Council, p.690.
Jayasinghe, T. (2011). Prediction of Time-dependent Deformations in Post-tensioned Concrete Suspended
Beams and Slabs in Tall Buildings, Doctoral dissertation, School of Civil, Environmental and Chemical
Engineering, RMIT University, Australia.
Rodriguez-Gutierrez, J. A. and Aristizabal-Ochoa, J. D. (2007). Short- and Long-Term Deflections in
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