Effect of Concrete Strength and Reinforcement on

Effect of Concrete Strength and Reinforcement on Time-Dependent Deflection of Posttensioned Slabs Behnam Vakhshouri, A.M.ASCE1 Abstract: Posttensioning is an effective construction method for structures with large spans, intensive loadings, and cost-efficiency considerations. The investigation developed a comprehensive understanding of how various reinforcement ratios and compressive strengths of concrete contribute to deflection of posttensioned two-way slabs. Furthermore, the numerical analysis compared the efficiency of various codes of practice to design the required reinforcement ratio in the presence of constant posttensioning tendons ratio and layout to provide the strength and deflection requirement. The interaction between the compressive strength–deflection and reinforcement ratio–deflection to find the optimum values of compressive strength and reinforcement ratio in a posttensioned two-way slab was also investigated. The finite-element model of a posttensioned 10 10 0.2-m (32.8 32.8 0.65-ft) two-way slab was analyzed and evaluated. The study confirmed the considerable effect of posttensioning to decrease the reinforcement ratio and deflection in a two-way slab. Also, a wide range of differences in design of a similar section of posttensioned concrete slab was observed by applying different codes of practice. The intensive effect of the concrete strength on the posttensioning design of slabs, especially in the lower ranges of compressive strength, was evident during the numerical analysis. Additionally, the reinforcement ratio shows a minor effect on the deflection of a posttensioned slab. DOI: 10.1061/(ASCE) SC.1943-5576.0000353. © 2017 American Society of Civil Engineers. Author keywords: Posttensioning; Two-way slab; Finite element; Compressive strength; Load-history deflection; Reinforcement.

Introduction Posttensioned concrete has been used in a wide range of building and civil structures since it was introduced in 1928 and first applied in a real construction project in 1950 (Cross 2007; Bondy 2012). The improved performance of concrete can allow longer spans, reduced structural thicknesses, and material savings compared to conventional reinforced concrete. Typical applications include high-rise buildings and parking structures, foundation systems, bridge and dam structures, silos and tanks, industrial pavements, and nuclear containment structures (PTI 2006; Kim et al. 2014). Application of posttensioned concrete is also an adequate engineering method to control the concrete cracking, especially in the negative bending moment regions (Su et al. 2015). Bonded posttensioned concrete is the descriptive term for a method of applying compression after pouring concrete and during the curing process (in situ). The bonded posttensioning significantly reduces the reinforcement requirements and provides higher ultimate strength due to the higher bond between the concrete and strands. It also provides better flexural crack distribution and good corrosion protection, and most importantly, it reduces the cost of the project (PTI 2006; Cross 2007). Instead of time-consuming and expensive empirical investigations, using a reliable finite-element program can effectively simulate the real behavior of the posttensioned concrete structure (Rabczuk and Zi 2008; Ayoub 2011). Kim et al. (2014) proposed a

1

Researcher, Centre for Built Infrastructure Research (CBIR), Univ. of Technology Sydney, Sydney, NSW 2007, Australia. E-mail: behnam [email protected] Note. This manuscript was submitted on May 2, 2017; approved on August 23, 2017; published online on November 30, 2017. Discussion period open until April 30, 2018; separate discussions must be submitted for individual papers. This paper is part of the Practice Periodical on Structural Design and Construction, © ASCE, ISSN 1084-0680. © ASCE

finite-element modeling method to simulate unbonded posttensioned concrete slabs. Despite uncertainties in the contact and friction behavior between the strands and sheathing, and the force-transfer mechanism in the anchorage system in the numerical simulation, they reported a good agreement between the numerical models and the experimental data in terms of the cracking pattern and stressdeflection variation. However, the model was not able to consider the friction losses and the exact tendon forces and balance loadings. Yu and Jeong (2014) numerically simulated the strand–concrete bond behavior of posttensioned concrete due to the chemical adhesion and friction. They found a strong dependency of the elastoplastic bond model due to the compressive strength of concrete. Also, the bond-transfer length recorded a decreasing rate by increasing the compressive strength of concrete. However, the time-dependent behavior of the posttensioned concrete was not predictable in their model. A similar study by Ayoub (2011) modeled a bond behavior in a posttensioned concrete slab. However, the long-term losses due to creep and shrinkage and the relaxation of tendons were not accounted for in the study. Joint investigations by researchers and design engineers, especially in recent years, has resulted in standards and recommendations aimed at developing the application of this method of construction in European countries, Australia, the United States, and throughout the Asian regions (Cross 2007). However, the problem is that the developed methods and relationships in different codes of practice sometimes give considerably different values of the reinforcement and tendons ratio for the same concrete structure. Correspondingly, considering the interaction between the mechanical properties of a posttensioned concrete structure, application of different design codes may change the structure response significantly (Larson et al. 2005). In view of the previously discussed investigations of posttensioned concrete slabs, this study presents the results of a numerical analysis of a long-span flat slab with different grades of concrete and reinforcement ratios. For a comparison basis, the slab thickness

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Pract. Period. Struct. Des. Constr., 2018, 23(1): 04017030

Pract. Period. Struct. Des. Constr.

and arrangement and ratio of the posttensioning tendons were considered to be constant in the analysis. The load-history deflection of slabs in the midspan and the designed reinforcement ratio were evaluated through different analyses. To design the posttensioned slab after analysis, the provisions in different codes of practice were utilized, and the required reinforcement and ratio in the slab were determined. The main objectives of this study were: • To simulate the bonded, posttensioned, two-way slab in a reliable numerical program to monitor the structure behavior and time-dependent deflection; • To compare the designed reinforcement ratio and the obtained time-dependent deflection at the midspan of the slab by applying the provisions in different codes of practice; • To investigate the relationship between the reinforcement ratio and the maximum time-dependent deflection of the posttensioned slab; and • To evaluate the interaction between the compressive strength, deflection, and reinforcement ratio in the presence of the constant posttensioning tendons ratio.

Principal Factors in Time-Dependent Deflection of Posttensioned Slabs Deflection in a reinforced concrete floor is affected by section size, elasticity of concrete, reinforcement ratio, and applied loading history. The combined effects of shrinkage and creep of concrete and the changing steel–concrete bond are the main parameters in the time-dependent behavior of a reinforced concrete structure. In a posttensioned concrete structure, the relaxation of posttensioning tendons causes additional gradual changes in the internal forces and deflection of the structure.

where « pi and « ci = strain in tendon and adjacent concrete at the time of bonding, respectively. It is assumed that all of the long-term losses of tendons, including relaxation and elastic shortening, occur before bonding in the RAM Concept program. Additionally, the structure weight is assumed to be eliminated by the equivalent upward force from the formwork. Consequently, the only acting forces in time-dependent behavior analysis of a posttensioned concrete structure are the forces resulting from balance loading in this program. Load Types Default loading types in this program are self-weight, posttensioning (balance and hyperstatic), and gravity loads; however, it is possible to include wind and seismic loads in the analysis and design process of the structure. In analysis of the slabs in this study, the applied dead and live loads were equal to 1.5 and 2.5 kPa (0.22– 0.36 psi) over the slab area, respectively. Different values of reduction factor of live load in the design of slabs by different codes of practice were considered. However, the irreducible live-load type was utilized, and no reduction factor was applied on the live load. Therefore, by applying equal loading values, the comparison of results is more accurate and meaningful. Codes of Practice

Traditional methods analyze the concrete floor slabs by approximating a region of a slab as a frame or design strip. The frame/strip is then commonly analyzed by moment-distribution methods. There are two main limitations in the application of these traditional methods. The first problem is wholly analysis and design of the simulated frame, especially in the irregular structures. The second limitation is approximating the slab/column interaction in the frame analysis that gives no information regarding the force distribution across the design strip. RAM Concept V8i was used in this study to analyze the posttensioned slab. The program utilizes finite elements to model the entire posttensioned or reinforced concrete slab. Finite-element analysis satisfies all equilibrium requirements, regardless of the structure’s irregularities.

Design of posttensioned concrete structures by applying regulations from a wide range of globally accepted codes of practice is a distinguished advantage of RAM Concept. This facility enables the users, especially the researchers, to perform a comprehensive comparison of the effective parameters in the design of posttensioned concrete structures. The available codes of practice in RAM Concept are American codes [ACI-318-99 (ACI 1999), ACI-318-02 (ACI 2002), ACI-318-05 (ACI 2005), ACI-318-08 (ACI 2008), and ACI318-11 (ACI 2011)], Australian standard [AS-3600-09 (Standards Australia 2009)], British standard [BS-8110-1 (BSI 1997)], Indian standard [IS-456-2000 (BIS 2000)], and Canadian standard [CSA. A23.3-04 (CSA 2010)]. Different combinations of the applied loads and the various models to estimate the mechanical properties of concrete and tendons before and after transfer are the main sources of differences in the design of posttensioned concrete structures by implementing the regulations in different design codes. Table 1 shows the load combinations to design the posttensioned concrete structure for the ultimate limit state (ULS) and sustaining service level (SSL) in the aforementioned codes of practice. Modulus of elasticity and tensile strength are the main parameters of concrete in design of the posttensioned concrete section. Table 2 compares the existing models in different codes of practice to estimate the modulus of elasticity and allowed limit of tensile strength of concrete in the initial service stage and all other conditions.

Posttensioning Systems in RAM Concept

Load-History Deflection

The RAM Concept program considers both bonded and unbounded tendon systems. In the bonded system used in this study, the bare strands are grouted within the ducts. In the unbonded system, the greased strands are encased in plastic sheathing. Because of the bonding effect, the strain in a bonded tendon is different from the strain in the adjacent concrete. The corresponding strain in a tendon (« p) and the strain in adjacent concrete (« c) are illustrated in Eq. (1)

The posttensioning causes less deflection and limited extent of cracking in the posttensioned slabs compared to the conventionally reinforced concrete slabs. In other words, the posttensioning system minimizes the cracking, and therefore, elastic deflection calculation methods have generally been acceptable. The long-term deflection of slab in RAM Concept is calculated by modification of the section stiffness by load-history variation. The load-history deflection calculation in RAM Concept assesses the effects of creep and shrinkage, tension stiffening, and load history on the time-dependent curvature of cross section. Then, it applies the results to modify the

RAM Concept Program

ɛp ¼ ɛc þ ðɛpi ɛci Þ © ASCE

(1)

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Table 1. Combination Factors of Applied Loads in SSL and ULS Design code ACI-318-99 (ACI 1999) ACI-318-02 (ACI 2002) ACI-318-05 (ACI 2005) ACI-318-08 (ACI 2008) ACI-318-11 (ACI 2011) AS-3600-09 (Standards Australia 2009) BS-8110-1 (BSI 1997) IS.456 (BIS 2000)

Design level

Self-weight

Dead load

Live load

Balance load

SSL ULS SSL ULS SSL ULS SSL ULS SSL ULS SSL ULS SSL ULS SSL ULS

1.0 1.4 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.4 1.0 1.5

1.0 1.4 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.2 1.0 1.4 1.0 1.5

0.5 1.7 0.5 1.6 0.5 1.6 0.5 1.6 0.5 1.6 0.4 1.5 0.5 1.6 0.5 1.5

1.0

Hyperstatic load 1.0

1.0 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Table 2. Modulus of Elasticity and Tensile Strength in Codes of Practice at Different Stages of Posttensioning Modulus of elasticity Design code ACI-318-99 (ACI 1999) AS-3600-09 (Standards Australia 2009) BS-8110-1 (BSI 1997) IS.456 (BIS 2000) EC-2 (CEN 2004) CSA.A23.3-04 (CSA 2010)

Initial service (transfer) pffiffiffiffiffi Eci ¼ 33:w1:5 : fci pffiffiffiffiffiffiffi 1:5 Ecmi ¼ 0:043 w : fcmi

Tensile stress

All other conditions pffiffiffiffi Ec ¼ 33:w1:5 : fc pffiffiffiffiffiffi 1:5 Ecm ¼ 0:043 w : fcm

rffiffiffiffiffiffiffi fcui 1:5 pffiffiffiffiffiffi Eci ¼ 5;500 fcui 0:3 fcki þ 8 Eci ¼ 22;000 10 w 1:5 pffiffiffiffiffi Eci ¼ 3;300 fci þ 6;900 2;300 Eci ¼ 5;500

rffiffiffiffiffiffiffi fcu 1:5 pffiffiffiffiffi Ec ¼ 5;500 fcu 0:3 fck þ 8 Ec ¼ 22;000 10 r 1:5 pffiffiffiffi Ec ¼ 3;300 fc þ 6;900 2;300 Ec ¼ 5;500

Initial service (transfer) pffiffiffiffi ft 0:3 fc pffiffiffiffi f t 0:25 f c

All other conditions pffiffiffiffi ft 0:6 fc pffiffiffiffi f t 0:6 f c

pffiffiffiffiffiffi f t 0:36 f cu

pffiffiffiffiffiffi f t 0:6 f cu

pffiffiffiffiffi ft 0:25 fci

pffiffiffiffi ft 0:6 fc

Note: The equations are illustrated in SI units (1 m = 3.3 ft, 1 MPa = 145 psi, 1 kg/m3 = 0.062428 lb/ft3); fci = cylinder strength at stressing time (MPa, psi); fc = 28-day cylinder strength (MPa, psi); fcmi = mean value of cylinder strength at stressing time (MPa, psi); fcm = mean value of 28-day cylinder strength (MPa, psi); fcui = cube strength at stressing time (MPa, psi); fcu = 28-day cube strength (MPa, psi); fcki = characteristic cylinder strength at stressing (MPa, psi); fck = 28-day characteristic cylinder strength (MPa, psi); w, r : density of concrete (kN/m3, lb/ft3 and kg/m3, lb/ft3, respectively).

element stiffness to calculate the deflection contours by a linearelastic analysis. Difference between Load History Deflection and LongTerm Deflection The load-history deflection is commonly larger or smaller than the strip-based long-term deflection in the RAM Concept program. Both methods try to estimate the time-dependent deflection of a slab after a long period of time. The entirely different methodology is the main reason for the difference. The load-history deflection is smaller than the strip-based longterm deflection in the following conditions: 1. Considering the section curvature and failure, the maximum load might not be sustained through the calculation duration. Therefore, the real load history may give a smaller deflection after the specified duration. 2. Whether the section is cracked or not, the load-history deflection always considers the compression reinforcement in the section. © ASCE

3. Load-history deflection always utilizes the uncracked transformed properties where the section is not cracked. The following aspects make the load-history deflection greater than the strip-based long-term deflection: 1. Redistribution of forces in the load-history deflection leads to a realistic prediction of cracking in the structure. Cracking causes increased forces in the adjacent regions, which can, in turn, cause additional cracking. 2. Reinforcement applies full or partial restraints on the shrinkage of the uncracked section. Stress induced by this shrinkage is considered in the cracking and tension-stiffening calculations.

Numerical Analysis Slab Geometry For the strength, serviceability, durability, and fire-protection requirements of the long-span slab, a 200-mm slab thickness is frequently used in construction projects. Also, from an economic

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standpoint, the posttensioning is more effective when the spans exceed 7.0 m. Fig. 1 compares the span length and the relative cost of reinforced and posttensioned concrete slabs. Therefore, a twoway flat slab with dimensions of 10,000 10,000 mm (394 394 in.) and a thickness of 200 mm (8 in.) was selected as a commonly used floor structure for the numerical investigation in this study. The simulated two-way flat slab is supported by four circular columns of 500-mm (19.7-in.) diameter and 3,000-mm (118-in.) height. The columns above the slab improve the slab stiffness and reduce the flexural deflection. Therefore, to perform a conservative

analysis, no column is added above the slab. Additionally, there are no drop panel and column capitals in the model. Fig. 2 shows the slab model and the columns in the RAM Concept program environment. The slab geometry in millimeters, column positions, and loading are in symmetric conditions in the model. The structural system to be analyzed in RAM Concept is defined by the design strip segments in two main directions of longitude and latitude. The analysis segments are generally governed by the slab geometry, flexural behavior, and position of the columns and walls. Fig. 3 shows the longitude and latitude design strips of the two-way flat slab in the RAM Concept environment. Mesh Size In finite-element analysis, accuracy of the results and required time to process the model are strongly influenced by the finite-element size (mesh size). The model with finer mesh yields highly accurate results but may have a longer computing time. To evaluate the effect of mesh size on the analysis results with reasonable processing time, the slab was meshed by 0.2, 0.5, 0.8, 1.0, 1.5, and 2.0 m (0.66, 1.65, 2.62, 3.28, 4.92, and 6.56 ft) mesh sizes and analyzed. Because there was no considerable difference in the results by using finer mesh sizes, a mesh size of 1.0 m (3.28 ft) was selected to save analysis time and run the model under various conditions. Design of Posttensioning Tendons

Fig. 1. Cost comparison: reinforced versus posttensioned concrete flat slab (1.0 m = 3.3 ft)

To apply a posttensioning system, different sizes and numbers of tendons can be used in a duct. The tendons with 12.7-mm (0.5-in.) and 15.2-mm (0.6-in.) diameter strands are the most frequently used types in posttensioning of the slabs. The 12.7-mm (0.5-in.) strand poses a higher strength per unit weight compared to the 15.2-mm (0.6-in.) strand, which reduces the cost. Also, the higher flexibility

Fig. 2. Geometry of flat slab and supporting columns (1.0 m = 3.3 ft)

© ASCE

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Fig. 3. Design strips in slab model

Fig. 4. Arrangement of posttensioning tendons in longitude and latitude directions (25.4 mm = 1 in.)

of the 12.7-mm (0.5-in.) strand helps its installation. Therefore, in agreement with the usual construction projects, the 12.7-mm (0.5-in.) strand was selected to apply the bonded posttensioning system in the slab model. Fig. 4 shows the layout of the tendons in latitude and longitude directions. The tendons including 5 strands in each duct are distributed in equal spacing of 1500 mm (59 in) in both directions. In addition, the height of tendons from the soffit of the slab is shown in Fig. (4).

Results and Discussion Effect of Concrete Strength on Deflection of Slab at Midspan Fig. 5 shows the effect of the compressive strength of concrete on the maximum deflection of the slab at midspan. Except for © ASCE

European code Eurocode 2 [EC-2-04 (CEN 2004)], increasing the compressive strength significantly reduces the maximum timedependent deflection of the slab at midspan in all codes of practice. In analyses of the slab by applying the provisions and limitations in Canadian code CSA.A23.3-04, American code ACI-318-08, and the British standard BS-8110-1, it was found that, by increasing the compressive strength up to 250%, the maximum deflection decreases approximately 150%. A similar increment of compressive strength in Indian standard IS-456-2000 and Australian standard AS-3600-09 gives approximately 25% less value. According to EC-2-04, an increment of the compressive strength in the range of 20–32 MPa (2.9–6.64 ksi) causes a slight increase of the midspan deflection. Beyond 32 MPa (2.9 ksi), an increasing compressive strength up to 50 MPa (7.25 ksi) gives approximately 15% less deflection of the slab. The reducing effect of the improved compressive strength of concrete on the deflection of slab falls linearly in this range.

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Deflection at midspan (mm)

40

35

30

25

20 AS-3600-09 BS-8110-97 EC-2-04

15

ACI-318-11 IS-456-2000 CSA.A23-04

10 10

20

30

40

50

60

Compressive strength (MPa) Fig. 5. Effect of improved compressive strength on midspan deflection (1 MPa = 145 psi, 25.4 mm = 1 in.)

Fig. 6. Compressive strength ratio versus midspan deflection ratio (1 MPa = 145 psi, 25.4 mm = 1 in.)

A concrete strength of 32 MPa (4.64 ksi) is often used in construction projects. Therefore, 32-MPa (4.64-ksi) concrete slabs and the corresponding deflection were selected as the basis of comparison in this study. Fig. 6 compares the effect of increasing ratio of the compressive strength on the decreased ratio of load-history deflection. According to Fig. 6, on average, an increasing compressive strength below 32 MPa (4.64 ksi) has a greater effect on the load-history deflection of slabs. Except for EC-2-04, the loadhistory deflection ratio is affected by the ratio of the compressive strength in all codes of practice in a similar manner. Effect of Compressive Strength on Required Reinforcement Ratio Reducing the reinforcement ratio is a crucial parameter in posttensioned slabs. The reinforcement ratio in this study is described as the area of tensile and compression steel bars to the gross section of the slab. The designed tensile and compression bars in RAM Concept for strength and serviceability requirements include the controls for minimum strength, minimum shrinkage, shear and flexural strength, punching effect, and other code provisions. A compression steel bar increases the compression resistance of the section and, consequently, increases the cracking moment, effective moment of inertia, and flexural strength of the section. The long-term deflection of slabs is generally predicted as a multiple of the instantaneous deflection. The compression bar in the slab section decreases the creep and shrinkage effects and, consequently, gives lower values of the time-dependent deflection (Standards Australia 2009). Fig. 7 shows the variation of the designed reinforcement ratio in the posttensioned slab with different values of the compressive strength of concrete. In almost all codes of practice, a compressive strength beyond 40 MPa (5.8 ksi) shows no effect on the designed reinforcement ratios in the flat slab. However, increasing the compressive strength in the range of 20–40 MPa (2.9–5.8 ksi) causes significant decreases in the reinforcement ratio. Considering the same section of slab in the analysis by different codes of practice, a 2-times higher compressive strength in AS-3600-09 sharply decreases the required reinforcement ratio to a value approximately © ASCE

Fig. 7. Effect of improved compressive strength on the required reinforcement ratio in posttensioned slab (1 MPa = 145 psi, 1 tonne = 1.10231 U.S. tons)

20 times less. In EC-2-04 and IS-456-2000, 100% higher compressive strength resulted in only 5% of the initial reinforcement ratio. In ACI-318-11 and CSA.A23.3-04, compressive strength has no effect on the designed reinforcement ratio. In BS-8110-1, a 90% lower reinforcement ratio is the result of 100% increased compressive strength in the flat slab. Similar to Fig. 6, Fig. 8 compares the effect of increasing ratio of the compressive strength on the decreased weight (or ratio in a constant section) of reinforcement in the slabs. According to Fig. 7, on average, an increasing compressive strength below 32 MPa (4.64 ksi) has a slightly higher effect on the required reinforcement ratio in the slabs. Except for AS-3600-09, the designed reinforcement ratio is highly sensitive to the ratio of the compressive strength in a similar way in all codes of practice.

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Conclusions

Ratio at reinforcement weight (%)

120

100

80

60

ACI-318-11 AS-3600-09

40

BS-8110-97 IS-456-2000

20

EC-2-04 CSA.A23-04

0 100

110

120

130

140

150

160

Rao of compressive strength to 32 Mpa ( %) Fig. 8. Compressive strength ratio versus required reinforcement ratio (1 MPa = 145 psi)

Fig. 9. Effect of reinforcement ratio on midspan deflection in posttensioned slab (1 tonne = 1.10231 U.S. tons, 25.4 mm = 1 in.)

Posttensioning is an effective way to control the deflection and reduce the tensile stress and strain in concrete structures. The effects of compressive strength of concrete and reinforcement ratio in the presence of a constant ratio of posttensioning tendons on the timedependent deflection of a two-way flat slab were evaluated in this study. The RAM Concept program, capable of finite-element simulation of the posttensioned two-way slab, was utilized for numerical investigation. The equations to predict the material properties and strength limits in different codes of practice were implemented in the analysis of the slab, and the results were compared. The following conclusions can be drawn from the study: • The models in different codes of practice to predict the concrete properties in the initial and transfer stages and service stages are considerably different. Additionally, the combination of the gravity, imposed, and balance loading is significantly different in the codes of practice. These factors are the main reasons for dissimilar results of finite-element analysis by these codes of practice. • Finite-element mesh size finer than 1.0 m showed a minor effect on the analysis results; thus, a 1.0-m (3.3-ft) mesh size was applied to the slab in the analysis in the RAM Concept program. • Improving the compressive strength of concrete caused the reduction of deflection of the two-way slab. This effect is almost similar in all codes of practice except for EC-2-04. • Sensitivity of the load-history deflection to increment of the compressive strength of concrete below 32 MPa was highly observable. • Increasing the compressive strength beyond 40 MPa (5.8 ksi) showed no effect on reduction of the required reinforcement ratio with a constant ratio of the posttensioning tendons in a two-way flat slab. • In a posttensioned concrete slab, improving the compressive strength of concrete in the range of 20–40 MPa (2.9–5.8 ksi) has the most reduction effect on the required reinforcement ratio. AS-3600-09, EC-2-04, and IS-456-2000 have the highest effect in this range of compressive strength. • Increasing the compressive strength of concrete in CSA. A23.3-04 and ACI-318-11 has no meaningful effect on reduction of the required reinforcement ratio of the posttensioned slab. This conclusion is valid in the whole range of 20–50 MPa (2.9–7.25 ksi) compressive strength. • The deflection in a posttensioned slab is mainly controlled by the tendons, so the effect of reinforcement ratio comes next. In all codes of practice, the reinforcement ratio is governed by the minimum requirements of each code and the balancing load. • There was no evident effect of the reinforcement ratio on the deflection of a posttensioned two-way flat slab.

Effect of Reinforcement Ratio on Deflection at Midspan In a reinforced concrete slab, increasing the reinforcement ratio to some extent has a decreasing effect on the deflection at midspan. However, because the posttensioning system is the main parameter used to limit the deflection behavior in the posttensioned slab, the reinforcement ratio shows a minor effect in this regard. Fig. 9 shows the relationship between the load-history deflection at the midspan of the slab and the designed reinforcement weight in the slab. Apart from the lower boundary of the diagram for the minimum required reinforcement in the section in different design codes, there is no meaningful relationship between the increased reinforcement weight (or ratio) and the deflection at midspan. In designing the posttensioning system, the balancing load may change the ratio of reinforcement in the section. © ASCE

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Ayoub, A. (2011). “Nonlinear finite-element analysis of posttensioned concrete bridge girders.” J. Bridge Eng., 10.1061/(ASCE)BE.1943-5592 .0000157, 479–489. BIS (Bureau of Indian Standards). (2000). “Plain and reinforced concrete: Code of practice.” IS.456, New Delhi, India. Bondy, K. B. (2012). “Two-way post-tensioned slabs with bonded tendons.” PTI J., 8(2), 43–48. BSI (British Standards Institution). (1997). “Structural use of concrete, Part 14: Code of practice for design and construction.” BS-8110-1, London. CEN (European Committee for Standardization). (2004). “EN-1992-11:2004: Design of concrete structures, part 1: General rules and rules for buildings.” Eurocode 2, Brussels, Belgium. Cross, E. (2007). “Post-tensioning in building structures.” Concr. Aust., 33(4), 48–54. CSA (Canadian Standards Association). (2010). “Design of concrete structures.” CSA.A23.3-04, Mississauga, Canada. Kim, U., Huang, Y., Chakrabarti, P. R., and Kang, T. H. (2014). “Modeling of post-tensioned one-way and two-way slabs with unbonded tendons.” Comput. Concr., 13(5), 587–601.

© ASCE

Larson, K. H., Peterman, R. J., and Rasheed, H. A. (2005). “Strength-fatigue behavior of fiber reinforced polymer strengthened prestressed concrete T-beams.” J. Compos. Constr., 10.1061/(ASCE)1090-0268(2005)9: 4(313), 313–326. PTI (Post-Tensioning Institute). (2006). Post-tensioning manual, 6th Ed., Phoenix. Rabczuk, T., and Zi, G. (2008). “Numerical fracture analysis of prestressed concrete beams.” Int. J. Concr. Struct. Mater., 2(2), 153–160. RAM Concept V8i [Computer software]. Bentley Systems, Exton, PA. Standards Australia. (2009). “Concrete structures.” AS-3600-09, Sydney, Australia. Su, Q., Yang, G., and Bradford, M. A. (2015). “Behavior of a continuous composite box girder with a prefabricated prestressed-concrete slab in its hogging-moment region.” J. Bridge Eng., 10.1061/(ASCE)BE.1943 -5592.0000698, B4014004. Yu, H., and Jeong, D. Y. (2014). “Bond between smooth prestressing wires and concrete: Finite element model and transfer length analysis for pretensioned concrete crossties.” Structures Congress, ASCE, Reston, VA.

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