Applications of sustainable post-tensioned concrete slabs

Innov. Infrastruct. Solut. (2017) 2:42 DOI 10.1007/s41062-017-0075-6 TECHNICAL PAPER Applications of sustainable post-tensioned concrete slabs Amr A. Abdelrahman 1 Received: 4 May 2017 / Accepted: 2 June 2017 / Published online: 7 July 2017 Ó Springer International Publishing AG 2017 Abstract Post-tensioning is used for the last decades for different concrete elements such as slabs, beams, walls and mat foundations. For industrial and office buildings with large spans, application of post-tensioned, (PT), concrete floors is competitive to reinforced concrete. Use of PT slabs results in small sections, better serviceability, durable structures and faster construction compared to reinforced concrete construction. In some cases, it demonstrates an economic alternative to conventional concrete or steel floors. Post-tensioning concrete slabs are applied using either bonded or unbonded tendons. Bonded tendons is achieved by grouting the ducts containing the steel tendons after stressing. Consequently, the prestressing force is transmitted to the concrete by bond along the steel tendons. In unbonded tendons applications, the ducts are left after stressing without grouting and the force is transmitted at the anchorages of the prestressing steel. This paper introduces analysis, design and construction techniques of PT concrete floors. Computer model specifically made to design PT slabs satisfying the requirements of the code is introduced. Case studies carried out in Egypt and in the Gulf area in the last few years with particular application of post-tensioning are also introduced. These case studies include buildings of spans up to 24.0 ms, as well as water tank of 100,000 m 3 capacity. Recommendations and design guidelines of PT concrete slabs as well as the assessment of the current Egyptian code are highlighted. This paper was selected from GeoMEast 2017 Sustainable Civil Infrastructures: Innovative Infrastructure Geotechnology. & Amr A. Abdelrahman amr_abdelrahman@eng.asu.edu.eg 1 Concrete Structures and Chair of the Structural Engineering Department, Ain Shams University, Abasia, Cairo, Egypt Keywords Application Computer model Design Posttensioning Prestressed concrete Slabs Introduction Post-tensioned (PT) concrete floors are used on a large scale in residential and office buildings in North America, Europe, Fareast and Gulf area. Compared to conventional reinforced concrete (RC) floors, PT slabs provide less thickness, fast construction cycle for each floor, durable concrete and, consequently, cost-effective structure. Posttensioning utilizes high-quality high strength steel such that 1 kg of post-tensioning strand may replace 3 or 4 kg of ordinary non-prestressed reinforcement [1]. This can reduce congestion of steel reinforcement in concrete members. In Egypt, PT floors are not used on the same scale as in other countries, which may be attributed to the fact that until year 2001 there was no design code for prestressed concrete. However, it should be mentioned that research in prestressed concrete started in Egypt as early as in 1959 [2]. The edition of the Egyptian Code for Design and Construction of Reinforced Concrete Structures ECP 203-2001 [3] addresses design and constructional details of prestressed concrete elements. Post-tensioned slabs are constructed using either bonded or unbonded prestressing tendons. Bonded tendons can be achieved by grouting the ducts containing the steel tendons after stressing. Therefore, the prestressing force is transmitted to the concrete by bond along the prestressing steel reinforcement. This introduces compatibility between the prestressing steel and concrete, which means that after bonding any strain experienced by the concrete is experienced by the prestressing steel and vice versa. In unbonded tendons applications, the ducts are left after stressing

42 Page 2 of 12 Innov. Infrastruct. Solut. (2017) 2:42 without grouting and the force is transmitted at the anchorages of the reinforcement. This means that bond is deliberately prevented along the length of the tendon. Thus, concrete strains are not translated directly into similar strains in the prestressing steel. Corrosion protection of the unbonded prestressing steel should be carefully applied to improve the durability of the concrete. Failure of unbonded steel strands at the anchorage zone was monitored as a result of steel corrosion. This paper introduces analysis and design technique of PT floors according to ECP 203-2001 [3] and other current international codes [4, 5]. Computer model specifically made to calculate the prestressing forces, losses and stresses and to design statically indeterminate PT concrete members is presented. The paper also presents case studies constructed in Egypt and in the Gulf area with PT floors. The first case study is an office building consisting of two basements, ground, three typical floors and roof, which was completed in 2002. The typical floor has an area of 3200 m 2 with spacing between columns of 10.8 and 5.4 m in both directions. Posttensioned flat slab with thickness of 250 mm was used. The second case is an exhibition hall constructed in 2003 of two floors, 2400 m 2 per floor. The maximum spacing between columns is 17.0 and 16.0 m in the two directions. The floor is constructed using PT main and secondary beams and oneway RC slabs on the top. Another case study is presented where the typical floor has a distribution of the columns with the largest panel of 20.5 9 23.7 m. The floor is constructed with post-tensioned ribbed slab of 600 mm depth. The last case study is water tank, where the slab-on-ground was prestressed to minimize the dimension and the amount of used steel. Assessment of different design aspects of PT concrete members according to the current Egyptian [3] code with comparison to the ACI [4] and British [5] codes is also introduced. Different design recommendations and construction details are given. Analysis of post-tensioned flat slabs Thickness of PT flat slabs is chosen as span/40 to 50 with span/45 as most commonly used value for two-way flat slabs and span/40 for one way slabs [6]. Different analytical techniques are recommended by design codes [3 5] for post-tensioned flat slabs including finite element method and equivalent frame analysis method, which is similar to that used for RC flat plates. In the frame analysis method, the relative stiffness between columns and slabs should be taken into consideration. Distribution of the bending moments between the column and field s is carried out according to the percentages given by the code. A computer code was specifically made using visual basic and Spreadsheet MS Excel to perform the analysis of PT statically indeterminate concrete members, as shown in Fig. 1. The computer code is linked to a structural analysis program SAP2000 to calculate the straining actions in the members due to gravity, horizontal and prestressing loads. The computer code can also perform the design of PT members under service and ultimate loading conditions. The code applies the equivalent frame method as a design tool of PT slabs. It also calculates the losses of prestressing forces and serviceability limit states of PT members. Finally, it generates the eccentricities of the cable profile and links it with a drawing program AutoCAD for implementation in the drawings. The following discusses the analysis and design aspects of PT concrete slabs. Cable pattern Different cable layout may be used in flat slabs depending on the percentage of the prestressing steel in the column and field s, as shown in Fig. 2. Prestressing steel in the column may vary from 50 to 100% out of the total amount of steel. Steel layout shown in Fig. 2a represents 100% of the prestressing steel banded through columns in both directions, while the middle part of the slab is reinforced by normal steel reinforcement. Figure 2b represents 100% of the prestressing steel banded through columns in one direction and uniformly distributed in the other direction. 75% of the prestressing steel may be concentrated in the column s and 25% in the field s in both directions, as in Fig. 2c, or only in one direction and uniformly distributed in the other direction as in Fig. 2d. Choice of the cable layout depends on the dimensions of the concrete panel as well as on different constructibility aspects of the PT flat slab. For example in Fig. 2c, d, elevation of the cables in the x-direction should top the cables in the y-direction at certain locations and laid under the cables at other locations to achieve the designed eccentricity of the prestressing tendons. This certainly will complicate the process of laying out the cables. The most common cable pattern is shown in Fig. 2b, where cables in the y-direction are laid out first according to the designed profile and topped with the cables in the x-direction. For flat slabs with aspect ratio more than 1.5, the distributed tendons are laid out in the long direction and tendons in the short direction are concentrated above the columns, as shown in Fig. 2b. In that case, the slab will act as a one-way slab in the long direction supported on embedded beams in the short direction. Cable profile Profile of the prestressing tendons should be carefully selected to optimize the number of steel strands. Figure 3 shows the general profile of a tendon in one panel. Three curves are used to characterize the profile using a parabolic shape described by the expression given in Eq. 1 for each

Innov. Infrastruct. Solut. (2017) 2:42 Page 3 of 12 42 Fig. 1 Computer code solving the cable profile curve. Length of curves 1 and 3 jjl is determined to satisfy the minimum radius R of the prestressing cables. The value of jj shown in Fig. 3 is typically taken between 0.05 and 0.1. y i ¼ a i x 2 i þ b i x i þ c i ð1þ where y i and x i are the eccentricity and distance of the tendon of the curve i, respectively. a i, b i and c i are constants. i = 1, 2 or 3. Constraints defining the cable profile are given for the curves in Eqs. 2 10. Based on the selected concrete cover and thickness of the ducts, the eccentricities at sections Introduction, Design of PT floors and Conclusions are assumed (Eqs. 2, 3, 4). Concrete cover is selected to satisfy both the fire rating and durability of the building. The eccentricity and tangent of curves 1 and 2 at point 2 should be the same (Eqs. 5, 7), and of curves 2 and 3 at point 4 should also be the same (Eqs. 6, 8). The tangent of curves 1 and 3 at points 1 and 5 is assumed to be zero (Eqs. 9, 10). An iteration process is carried out to solve Eqs. 2 10 and the constants a, b and c given in Eq. 1 are determined for the three curves to describe the cable profile along the given span. Figure 1 shows the computer code established to describe the cable profile. y 1 ¼ e 1 ðfor curve 1Þ ð2þ y 3 ¼ e 3 ðfor curve 2Þ ð3þ y 5 ¼ e 5 ðfor curve 3Þ ð4þ y 2 ðfor curve 1Þ ¼ y 2 ðfor curve 2Þ ð5þ y 4 ðfor curve 2Þ ¼ y 4 ðfor curve 3Þ ð6þ dy dx dy dx dy dx dy dx for curve 1 ¼ 2 for curve 2 ¼ 3 ¼ 0 ðfor curve 1Þ 1 ¼ 0 ðfor curve 3Þ 5 Structural analysis dy dx dy dx for curve 2 2 for curve 3 4 ð7þ ð8þ ð9þ ð10þ The structure is divided into a series of frames in the x and y directions and solved to calculate the straining actions taking into consideration effect of prestressing

42 Page 4 of 12 Innov. Infrastruct. Solut. (2017) 2:42 Fig. 2 Cable pattern normal reinforcement tendons (a) 100% banded through columns in both directions and normal reinforcement (b) 100% banded through columns in one direction and uniform distribution in other direction middle column middle middle column middle (c) 75% concentrated in column and 25% in middle in both directions middle column middle (d) 75% concentrated in column and 25% in middle in one direction-other direction uniform Fig. 3 Cable profile 1 2 3 4 5 e 5 e e 3 1 R Curve (1) Curve (2) Curve (3) column βl (1-2β) L βl L forces. The computer code shown in Fig. 1 generates the required data of prestressing forces and eccentricities of the cables to be linked to a structural analysis program using FEM SAP2000. Effect of the prestressing force on the supporting elements is considered in the analysis. For high column stiffness, it is expected that a large bending moment due to prestressing is transferred to the columns; in addition, less prestressing force is transferred to the slabs. These forces will change by time due to creep of concrete and losses in the prestressing force. In some cases, the concrete area of the slab around the stiff columns or shear walls is cast after stressing the columns to reduce the losses in the prestressing force. More deformation is expected for the flexible columns and, consequently, larger axial force in the slabs due to prestressing.

Innov. Infrastruct. Solut. (2017) 2:42 Page 5 of 12 42 Design of PT floors Post-tensioned floors should be designed to satisfy allowable stresses in the concrete under service loading condition. Ultimate limit state of flexure, shear (one-way or punching shear) should be checked using factored loads. Serviceability limit states in terms of camber, deflection and vibration should also be checked. In addition, crack width and fatigue of prestressed and non-prestressed steel should be calculated in case of partial prestressing. The previously described computer code was extended for the design of statically indeterminate PT elements including service and ultimate limit states. The computer code can solve any number of continuous spans and calculate the prestress losses, service stresses and required additional non-prestressing steel. Service stresses in concrete A major difference exists between design codes since the Egyptian code [3] does not allow partial prestressing; i.e., no cracks are allowed in the prestressed concrete members under service loading. It is the author s understanding that partial prestressing was not allowed in the code since it is only the first edition for prestressed concrete code in Egypt and it will be included in the coming issue. In the ACI code [4], partial prestressing is not allowed in prestressed twoway slabs but allowed in all other members. The British Standards [5] allows three classes for prestressed members; class 1 where no tensile stresses are allowed, class 2 where tensile stresses are still below the rupture strength of concrete and class 3 where concrete sections are allowed to crack. The difference in the allowable values of concrete stresses under initial and final loading conditions is minor in the three design codes. Ultimate limit state of flexure One of the most crucial issues in the design of statically indeterminate prestressed members is the effect of secondary moment (M r ) on the ultimate limit state of flexure. The secondary moment is the moment resulting from the reactions induced by prestressing forces, and can be calculated as the difference between the moment due to prestressing (M f ) minus the primary moment (M o ) resulting from the product of the prestressing force and eccentricity of the cable, as given in Eq. 11. M r ¼ M f M o ð11þ The secondary moment is significant in both the elastic and inelastic states. The elastic deformations caused by a non-concordant tendon change the amount of inelastic rotation required to obtain a given amount of moment redistribution. Conversely, for a member with a given inelastic rotational capacity, the amount by which the moment at the support may be varied is changed by an amount equal to the secondary moment at the support due to prestressing. Therefore, the secondary moments should be included in determining design moments [7]. The ACI code states that moments used to compute required strength shall be the sum of the secondary moments (with a load factor of 1.0) and the moments due to factored loads. The ACI also permits to increase or decrease negative moments calculated by elastic theory for any assumed loading, where bonded reinforcement is provided at supports. It shall be permitted to increase or decrease negative moments calculated by elastic theory at supports of continuous flexural members for any assumed loading arrangement by not more than 1000 jj t %, with a maximum of 20%. Redistribution of negative moments shall be made only when jj t is equal to or greater than 0.0075 at the section at which moment is reduced. jj t is the net tensile strain in extreme tension steel at nominal strength excluding the strains due to effective prestress, creep, shrinkage, and temperature. The commentary of the ACI code states, When hinges and full redistribution of moments occur to create a statically determinate structure, secondary moments disappear. Bondy [7] introduced an analytical approach to show that the secondary moments do not disappear at any load level. The Egyptian code ECP 203-2001 does not address the effect of secondary moment on the ultimate limit state of flexure. Ultimate limit state of shear Both one-way and two-way (punching) shear of PT flat slabs should be checked using limit state design. Prestressing has a marked increase on the resistance of concrete sections to shear forces. The ACI and British codes permit the use of shear reinforcement in the slabs in the form of bars or wires and single- or multiple-leg stirrups in slabs. The Egyptian code ECP 203-2001 addresses oneway and two-way shear for prestressed members. The code does not also allow use of steel reinforcement to resist punching shear stresses in the slabs. Serviceability limit states Both camber and deflection of fully prestressed members are calculated based on the gross moment of inertia. However, for partially prestressed members the inertia should be reduced to account for cracks. The ACI code recommends the bi-linear moment-deflection relationship or an effective moment of inertia (I e ) method to calculate the deflection. The British code recommends using the

42 Page 6 of 12 Innov. Infrastruct. Solut. (2017) 2:42 Moment curvature curve for deflection calculation of partially prestressed members. Case studies Case studies are presented in this paper. The first case study is an office building, where PT flat slab was used with banded tendons in one direction and distributed tendons in the other. The second study is an exhibition hall with a limited clear height and large spans between the columns. PT main and secondary beams were used to cover the accessible slabs. Considerable savings in cost and time were achieved in the construction of the two structures. In the third case study, a larger panel of dimensions 20.5 9 23.7 m was constructed using post-tensioned ribbed slab with 600 mm depth. The last case is a water tank with overall dimensions 100 9 200 m in plan. The slabon-ground with thickness of 300/600 mm was post-tensioned in both directions. First case study The first case study is an office building, which consists of two basements, ground, three typical floors and a roof. The typical floor has an area of 3200 m 2 with spacing between columns of 10.8 and 5.4 m in both directions. The building was divided into three parts by two expansion joints, as shown in Figs. 4 and 5. The structural design of the floors in the tender document included one-way ribbed slab and embedded RC beams. The contractor was challenged to finish the project in 9 months and was faced by an unexpected increase in the price of steel reinforcement. Posttensioned flat slab with thickness of 250 mm was proposed to substitute the RC slab. RC beams were used on the Fig. 4 Plan of the 1st case study Fig. 5 Aerial view of the 1st case study outside perimeter of the building to maintain the architectural appearance of the façade. The project was completed on time with considerable savings in the cost of floor slabs. Construction details Selection of the cable pattern was based on the rectangularity of the slabs. A total of five banded prestressing steel tendons were located in the short direction; i.e., in the direction of 5.40 m spans between columns. Distributed tendons every 1.35 m were placed in the long direction of the slab, as shown in Fig. 6. Four and three prestressing steel strands of 15 mm diameter were used in the banded and distributed tendons, respectively. The prestressing steel conformed to the ASTM A416 with tensile strength and strain of 1860 MPa and 3.5%, respectively. The strands were placed in galvanized steel ducts with overall dimensions of 80 9 20 mm. Steel bars of 10 mm diameter were 55 67 PART 2 59.40 PART 1 PART 3 58.56 115.40 8 x 5.4 = 43.2

Innov. Infrastruct. Solut. (2017) 2:42 Page 7 of 12 42 Fig. 6 Details of the prestressing steel Fig. 9 Dead end free edge regions not prestressed in direction parallel to tendons banded tendons Fig. 7 Profiling of the steel tendons Fig. 10 Non-prestressed regions in slabs Fig. 8 Jacking end Fig. 11 Casting concrete slabs

42 Page 8 of 12 Innov. Infrastruct. Solut. (2017) 2:42 Fig. 12 Structural plan of the exhibition hall 13.6 Main beam secondary beams 16.0 40.5 Main beam 10.9 11.0 17.0 59.9 17.0 14.9 Fig. 13 Overview of the floor slab before casting concrete used as chairs with varying heights to shape the profile of the tendons, as shown in Fig. 7. The jacking and dead ends of the prestressing steel tendons are shown in Figs. 8 and 9, respectively. Special reinforcement was used around the end blocks to resist the splitting tensile stresses induced from the prestressing forces. Additional non-prestressed steel was used on top of the columns to ensure enough flexural capacity at ultimate loads. Unlike the distributed tendons, the banded tendons induce compressive stresses that are not uniform on the edge of the slab, as shown in Fig. 10. Additional nonprestressed steel reinforcement of 10 mm diameter every 160 mm was placed perpendicular to the free edge in the non-prestressed zones. Concrete with characteristic cube strength of 40 MPa after 28 days was used to cast the slabs, as shown in Fig. 11. Curing compound was applied on the concrete surface directly after casting to minimize the tensile stresses due to shrinkage. Fig. 14 Details of the intersection between main and secondary beams Fig. 15 View of the case study number 3 After the concrete had reached 30 MPa, which was normally achieved in 3 days, the steel strands were tensioned to 75% of its ultimate tensile strength. Elongations of the strands were measured and compared to the calculated values. Once the prestressing forces were applied, the

Innov. Infrastruct. Solut. (2017) 2:42 Page 9 of 12 42 formwork was removed and assembled for the next floor. Ducts containing the prestressing steel strands were grouted with a flowable mix with 40 MPa compressive strength. Construction cycle of each part of the floor slab took only 7 days. Second case study The second case study is an exhibition hall constructed of two floors with an area of 2400 m 2 per floor. The maximum spacing between columns is 17.0 and 16.0 m in the two directions, as shown in Fig. 12. Maximum thickness of floors was selected to maintain the clear height given by the architect. Due to the limited height of floors, RC frames were not a structural alternative. Two structural systems of the floor slabs were studied. The first system was composite steel beams and concrete slabs and the second was post-tensioned main and secondary beams with one-way RC slab on top. The second system was selected due to its cost effectiveness and durability. Two four-span continuous main beams were used to support a group of secondary beams. The main beams were Fig. 16 a Plan of the typical PT concrete floor with banded tendons. b Plan of the typical PT concrete floor with distributed tendons (a) (b)

42 Page 10 of 12 Innov. Infrastruct. Solut. (2017) 2:42 16.0 m apart, while the secondary beams were spaced every 3.0 m. Post-tensioned beams were designed to be fully prestressed tensile stresses under service loading according to the ECP 203-2001. Ultimate limit states of flexure and shear were checked and additional reinforcement was placed at the columns and mid-spans. Constructional details The main beams were 1500 mm wide and 1100 mm deep, while the secondary beams had a varying width of 400 600 mm and a depth of 700 mm. The varying width of the secondary beams was mainly to allow for the extra reinforcement placed at the end blocks of the prestressing forces. The one-way RC slab used on top was 160 mm thick. Five prestressing steel cables with 12 steel strands per one were used to prestress each main beam. Ducts used in the main beams were circular of 90 mm diameter. Two prestressing steel cables of eight steel strands per each were used in the secondary beams. Seven wire steel strands of 15 mm diameter conforming to ASTM A416 were used. Figure 13 shows an overview of the floor slab before casting concrete. Details of the intersection between the main and secondary beams are shown in Fig. 14. The characteristic concrete strength was 35 MPa after 28 days and 30 MPa at time of prestressing. The prestressing sequence of the cables was designed to maintain minimum straining actions in the beams during tensioning. 50% of the cables in the main beams were tensioned first, followed by full force in the secondary beams. The remaining part of the prestressing forces in the beams was jacked. After ping the formwork of the first floor, Props were left to support the slab to help carrying the weight of the concrete slab in the second floor. Third case study The first LEED certified project in Egypt and Africa; the 21,000 m 2 LEED Gold Certified HSBC Egypt Global Service Centre is a four-story building with two levels of underground parking located in Egypt s Smart Village Cairo master-planned development. The building serves as a regional and global hub for HSBC s Middle East and Europe and has been designed and constructed to LEED standards (Leadership in Energy and Environmental Design) an international green building rating system by USGBC (United States Green Building Council). The building consists of two basements, ground and three typical floors with semi-circle shape in plan, as shown in Fig. 15. Fig. 17 Typical plan of the office building 5T10/m` 5T10/m` 5T10/m` 5T10/m` Min.2cm Mortar Fig. 18 Typical cross section of the slab

Innov. Infrastruct. Solut. (2017) 2:42 Page 11 of 12 42 prestressing pattern of the concrete floors was chosen so that the distributed tendons were in the radial direction, while the banded tendons were in the tangential direction, as shown in the figure. Fourth case study Fig. 19 Plan of a typical panel in the slab The fourth case study is an office building, which consists of two basements, ground, three typical floors and a roof. The typical floor has an area of 9000 m 2 with spacing between columns up to 20.5 9 23.7 m. The building was divided into three parts, as shown in Fig. 17. The slab is a ribbed slab with a depth of only 600 mm and Prestressed in both directions and supported on embedded post-tensioned beams with 600 mm depth, as shown in Figs. 18 and 19. The choice of this structural system allowed for a minimum depth to result in the largest possible clear height of the floor. Due to the small stiffness of the slab, a detailed vibrational analysis of the slab was carried out to provide comfort for the users of the building. The project was successfully completed in 2014. Fifth case study Fig. 20 Plan of the water tank showing sequence of construction The total length of the curved façade was 125 m, which was divided into three parts with pour s, as shown in Fig. 16. Each part was cast separately in order to minimize the concrete shrinkage effect on the floors and columns. The pour s separating the adjacent parts were cast after 30 days from casting the last concrete part. The The fourth case study is a water tank with overall dimensions of 200 9 100 m divided by expansion joints into 15 parts, as shown in Fig. 20. The slab-on-ground has a variable thickness of 300/600 mm, while the elevated slab has a variable thickness of 280/400 mm, as shown in Fig. 21. Both slabs were post-tensioned in both directions using banded tendons in one direction and distributed tendons in the other direction. Computation of the losses in the prestressing force due to friction with the soil was a challenging parameter in the design. Overestimating the friction between the slab-on-ground and the soil will result in less compression on the concrete slab than the actual value. Sequence of casting was carefully selected, asshowninfig.20, in order to minimize the cold joints in the slab. Several concrete pockets were introduced to allow for prestressing when an adjacent part is already cast. Fig. 21 Typical cross section of the water tank

42 Page 12 of 12 Innov. Infrastruct. Solut. (2017) 2:42 Conclusions A computer code was made to optimize the prestressing cable profile and design of statically indeterminate posttensioned slabs. The Egyptian Code for Design and Construction of Reinforced Concrete Structures ECP 203-2001 addresses design of PT members. Several case studies are presented proving the feasibility of post-tensioned slabs in terms of cost and construction time. References Division of the South African Institution of Civil Engineering and the Institution of Structural Engineers 2. Aboueleied A (1958) An investigation of two-span continuous prestressed concrete beams, M.Sc Thesis, Cairo University, p 200 3. Ministry of Housing, Utilities and Urban Communities (2001) The Egyptian Code for Design and Construction of Reinforced Concrete Structures ECP 203-2001, Ministerial No. 208, 2nd edn 4. American Concrete Institute (2002) Building code requirements for structural concrete (ACI 318 m-02) and commentary (ACI 318rm-02), p 445 5. British Standards Institution (1997) Structural use of concrete, part 1. Code of practice for design and construction, BS-8110 6. Collins MP, Mitchel D (1997) Prestressed concrete structures. Response Publications, London 7. Bondy K (2003) Moment redistribution: principles and practice using ACI 318-02. PTI J: 3 21 1. The South African Institution of Civil Engineering (2001) Design of prestressed concrete flat slabs. Report of Joint Structural