reinforced concrete floor system

Behaviour and Design of Reinforced Concrete FloorSystemsA ThesisSubmitted in Partial Fulfillment of the RequirementsFor the Degree ofBachelor of Civil EngineeringByLiang LIU307005798Supervisor: Dr Gianluca RanziSchool of Civil EngineeringUniversity of Sydney, NSW 2006AustraliaOctober 2010DisclaimerThis thesis was prepared for the School of Civil Engineering at the University of Sydney, Australia, and describes parametric study of reinforced concrete floor systems. The opinions, conclusions and recommendations presented herein are those of the University of Sydney or any of the sponsoring parties to this project.The work comprising this thesis is substantially my own, and to the extent that any part of this work is not my own I have indicated that it is not my own by acknowledging the source of the part or those parts of the work.I have read and understood the University of Sydney Student Plagiarism: Coursework Policy and Procedure.I understand that failure to comply with the University of Sydney Student Plagiarism: Coursework Policy and Procedure can lead to the University commencing proceedings against me for potential student misconduct under Chapter 8 of the University of Sydney By Law 1999 (as amended).Liang Liu307005798iiACKNOWLEDGEMENTSI would like to express my sincerest appreciation to my thesis supervisor, Dr. Gianluca Ranzi, for his great guidance, insightful advice, expect instruction and patient. I learned so much from the fruitful conversation with him which makes this study period an enjoyable.I would also like to thank to my teammates, Xiaoqi Zhuang and Sunnie Chen, for sharing joys and tears through this thesis experience. It is effective to study and much easier to compare and analyse results with their incredible idea and thoughtful suggestion.iiiSUMMARYThis thesis investigates the behaviour and design of reinforced concrete floor systems which consist of reinforced concrete slabs and beams. Selecting the most effective floor system can significantly minimize construction time and reduce construction costs, especially for building and construction industry.The parametric study particular emphasis on the strength and serviceability behaviour of one way slab, two way slab and flat slab floor systems and intends to investigate three floor systems through comparing slab thickness, reinforcement weight and total concrete volume. The slabs and beams design of these floor systems is carried out in accordance with AS3600. These parametric studies are further investigated by varying the live load, span length, material strength and reinforcement ratio.It was found that the deflection ratio diminishes sharply as live load increases in both one-way slab and two-way slab. The useful design graphs are developed to help designers quickly in selecting an appropriate floor system. The study also found that the flexural strength enhances and the total deflection becomes larger as the reinforcement ratio increases. The implications that this may have on design and any possible suggestions are discussed.ivCONTENTSList of Figures (viii)List of Tables (x)Chapter 1 Introduction……………………………………………………………..………P11.1 General…………………………………………………………………../……….P11.2Objectives ………………………………………………………………….…….P3Chapter 2 Literature Review………………………………………………………/………P42.1Reinforced concrete floor systems………………………………………………P42.2Reinforced concrete slab…………………………………….………........…….P62.3Reinforced concrete beam……………………………………………..……….P9Chapter 3 Methodology……………………………………………………………..……..P113.1Notations……………………………………………………………………….P113.2Combinations of Actions………………………………………………..……..P133.3Limits on Material Strength…………………………………………..………..P133.4Strength Safety Factors………………………………………………...………P143.5Beam Design Procedure…………..…………………………………...……….P143.5.1Design Flexural Reinforcement……………………………………….P143.5.1.1Determine Bending Moment ………………………………………P143.5.1.2Determine Required Flexural Reinforcement…………………...…P153.5.1.2.1Design of Rectangular Beams………………………….....P163.5.1.2.2Design of Flanged Beams……………………………..….P17v3.5.1.2.2.1T Beam Under Negative Moment……………..…….P183.5.1.2.2.2T Beam Under Positive Moment……………...……..P183.6Slab Design Procedure…………………………………………………..…….P203.6.1Strength ……………………………………………………….…….P213.6.1.1Flexural Strength……………………………………………..…..P213.6.1.2Flexural Shear……………………………………………….……P213.6.2Serviceability…………………………………………………..…….P213.6.2.1Deflection control…………………………………………..…….P213.6.2.2Crack control……………………………………………………..P223.6.2.3Deemed-to-comply method………………………………..…….P233.6.2.4Simplified method……………………………………………….P24Chapter 4 Parametric Study………………………………………………………………P254.1 Structural plan views…………………………………………………………..P264.2 Standard case parameters…………………………………………………..…..P274.3 Various parameters…………………………………………………………….P284.4 Results…………………………………………………………………………P284.4.1 Standard case results…………………………………………………..P284.4.1.2 Beam design results…………………………………………...….P284.4.1.3 One way slab results……………………………………….……..P294.4.1.4 Two way slab results……………………………………………..P294.4.1.5 Flat slab results……………………………………………...……P294.4.2 Various live loads and spans results…………………………….…..…P304.4.3 Various reinforcement ratio results in two way slabs………………....P334.4.4 Various material strength…………………………………………...…P36vi4.4.5 Three floor systems comparing………………………………………..P374.4.6 Design graphs………………………………………………….………P39 Chapter 5 Case study………………………………………………………………….…..P41Chapter 6 Conclusion……………………………………………………………….……..P43References……………………………………………………………………………..……P45Appendix A One Way Slab Design Matlab Code (I)Appendix B Two Way Slab Design Matlab Code (IX)Appendix C Flat Slab Design Matlab Code (XVII)Appendix D Beam Design Matlab Code (XXIX)Appendix E Coefficients for Rectangular S labs (XXXII)viiList of FiguresFigure 1.2 Reinforced floor systems………………………………………………………….P1 Figure 2.2 Design moments and shear………………………………………………………..P4 Figure 2.3 Minimum slab thickness for two way slab system………………………………..P5 Figure 2.4. Variation in maximum span to depth ratio based on longitudinal reinforcement ratio………………………………………………………………………………………..….P8 Figure 3-1. Rectangular beam design…………………………………………………….…P16 Figure 3-2. T beam design…………………………………………………………………..P18 Figure 4.1 One way slab plan view…………………………………………………..……..P25 Figure 4.2 Two way slab plan view…………………………………………………………P26 Figure 4.3 Flat slab plan view……………………………………………………………….P26 Figure 4.4 Safety ratios vs live load for one way slab and two way slab…………...………P31 Figure 4.5 Safety ratios vs span for one way slab and two way slab………………………..P32 Figure 4.6 Safety ratios vs span and live load for flat slab………………………………….P33 Figure 4.7 Moment ratios vs span for two-way slab for various reinforcement ratio………P34 Figure 4.8 Deflection ratios vs span for two-way slab for various reinforcement ratio…….P35 Figure 4.9 Design graph for 3 kPa live load………………………………………………...P38 Figure 4.10 One way slab design graph……………………………………………………..P39 Figure 4.11 Two way slab design graph…………………………………………………….P40 Figure 4.12 Flat slab design graph……………………………………………………….….P40viiiFigure 4.13 One way slab floor plan top view for case study…………………………..…..P41 Figure 4.14 Two way slab floor plan top view for case study………………………..……..P41 Figure 4.15 Flat slab floor plan top view for case study…………………………….………P42 Figure 4.16 Material quantities comparing for case study…………………………………..P42ixList of TablesTable 3.1 Minimum Requirement of Reinforcement for Crack Control………………...….P23 Table 4.1 Standard case parameters……………………………………………………...….P27 Table 4.2 Variables in the floor systems……………………………………………….……P28 Table 4.3 Beam results for standard case ……………………………………………….….P28 Table 4.4 One way slab results for standard case……………………………………..…….P29 Table 4.5 Two way slab results for standard case…………………………………………..P29 Table 4.6 Flat slab results for standard case…………………………………………….…..P29 Table 4.7 Two way slab results for various spans…………………………………………..P30 Table 4.8 Two way slab results for various live loads…………………………………...….P31 Table 4.9 Moment ratios vs span for two-way slab for various reinforcement ratio……..…P34 Table 4.10 Deflection ratios vs span for two-way slab for various reinforcement ratio……P35 Table 4.11 Slab thickness with increasing concrete strength…………………………….…P36 Table 4.12 Slab thickness with increasing steel reinforcement strength………………..…..P37 Table 4.13 Three floor systems comparing………………………………………………....P38xChapter 1 Introduction1.1GeneralReinforced concrete floor systems have been gaining more and more popularity in thebuilding and construction industry, particularly over the past two decades. The choice of different reinforced concrete floor system which is shown in Figure 1.2 below is an important economic decision in a building and plays a major role of ease and speed of construction.Figure 1.2 Reinforced floor systems (L.A. Prieto.Portar, 2008)Due to the complexity of reinforced concrete floor systems design, this study only designs and investigates one-way slab, two-way slab and flat slab floor systems in order to select themost efficient floor system in accordance with Australian Standards.1The design of reinforced concrete floor systems requires the designers to not only understand the behaviour of the individual components of the reinforced concrete and the floor system, but also the relationship between the two components. Reinforced concrete consists of steel and concrete which is a commonly used material for slabs and beams in the building. For reinforced concrete, the prime serviceability considerations relate to deflections and cracking of the concrete. Deflection control and crack control both require a study of the stresses and deformations that occur in cross-sections. On the other hand, floor system is a system formed by slabs, beams, joists or girders, which separates the stories of a building. To obtain an understanding of the behaviour of the frame in the floor system under horizontal load, it is important to realise that the floor system at each level acts as a rigid diaphragm. This means that the columns and the walls are effectively tied together and therefore move together at each floor level without any relative movement between individual columns. The vertical loads can transmit to supporting beams, footings and columns through one-way and two-way action occur in the slabs. Therefore, designers should develop a logical understanding of reinforced concrete slabs and beams and all the important factors in the floor systems which may affect the designs in order to design the reinforced concrete floor systems appropriately. In Australia, as for most countries, limit state design concepts are used to define acceptable minimum levels of performance that reinforced concrete floor systems must achieve for strength and serviceability, and also for other design requirements such as durability and fire resistance. In order to proceed with the detailed design of the individual components of a reinforced concrete floor system it is first necessary to translate the design requirements of strength and serviceability into quantitative criteria.21.2 ObjectivesThe objectives of this thesis are to investigate the behaviour of reinforced concrete floor systems under strength and serviceability criteria. This study will consider the design of slabs and beams accordance with Australian Standards in order to yield realistic results. The following aspects will be focused during the process of conceptual development of the reinforced concrete floor systems design:∙To design one-way slab, two-way slab and flat slab floor systems in accordance with the limit state design method given by AS3600. A computing program MATLAB is utilized and a Microsoft Excel Spreadsheet is developed in order to compare the results.∙To investigate how strength limit state or serviceability limit state governs the design of different floor systems with various parameters. For this purpose, live load, span, material strengths and reinforcement ratio will be selected as variables.∙To explore the advantages and disadvantages of each floor system through determining and comparing minimum slab thickness, reinforcement weight and total concrete volume∙To develop useful design graphs to help designers quickly in selecting an appropriate floor system.34Chapter 2 Literature review2.1 Reinforced concrete floor systemsIn 2007, David et al addressed the design of reinforced concrete floor systems. In their research, strength and serviceability were the major criteria which must be designed for the maximum effects of factored loads in the design of reinforced concrete floor systems. The design moments and shear forces in the design procedure could be determined from the Figure 2.2.Figure 2.2 Design moments and shear (David et al, 2007)Generally, the deflection requirements shall be satisfied by determining the minimum slab or beam thickness which could satisfy deflection criteria for all spans. The minimumslabthickness for two-way slab systems were shown in Figure 2.3 in David’s research for grade 60 reinforcement.Figure 2.3 Minimum slab thickness for two way slab systems (David et al, 2007)On the other hand, the reinforcing bars are the important parameters to design the reinforced floor systems. The reinforcing bars shall be developed properly once the required flexure and shear reinforcement have been determined. For a one way slab floor system, the main flexural reinforcement is placed in the shorter span, while secondary reinforcement is placed in the orthogonal direction to control cracking due to shrinkage and temperature effects. In contrast, a two way slab floor system has bending moments of comparable magnitude in both directions and requires flexural reinforcements in both directions. Additional parameters which are span length, floor loads, steel reinforcement ratio and material strength must be considered when selecting an economical floor system.5In 1972, Phillip also discussed that optimizing floor system design was greatly complicated by the variables parameters of the system. His article used two methods which were Simplified Method and Equivalent Frame Method to compare the different floor systems geometry, dimensions and types. The major parameters were investigated which were slab thickness, area of drop panel and span length by using these methods. In his research, it indicated that the columns spacing should not be selected if span ratio occurred at maximum span-length ratio of drop panel. And he also concluded that larger beam and slab ratio required smaller span- length ratio of drop panel in the floor systems. It was easier to select drop panel and calculate the material quantity required for the designers by using his research.2.2 Reinforced concrete slabReinforced concrete floor systems typically consist of a reinforced concrete slab placed upon reinforced concrete beams. The strength and serviceability are also the most important criteria in the reinforced concrete slabs.In the serviceability of slab systems, mid span deflection control is an important performance design. In 1996, Hwang et al investigated deflection control of two way reinforced concrete slabs. Two alternative design procedures for deflection control were discussed in their investigation. The mid span deflection could be directly calculated by a semiempirical method to ensure the magnitude within the permissible maximum deflection. This approach was more reasonable comparing the following one because of depending on elaborate deflection calculations. However, this method consisted of enormous number of parameters. The designer shall understand and minimize the number of variables so as to solve the problem. Alternatively, deflection was decided by adopting a slab thickness greater than a specified minimum value. The minimum thickness requirements controlled the slab deflections within allowable deflection limits in a similar format of allowable span depth ratios. This approach was more attractive than the first one for designers.In 2008, Tang et al had studied influence of longitudinal reinforcement strength on one way6slab deflection. They also used a method which was similar to the procedure of Hwang et al (1996) to check the deflection limit based on minimum member thickness requirements and a direct computation method. An integral part of the deflection calculations defined in the above method was an evaluation of an appropriate moment of inertia for the cross section in order to reflect the variable cracked nature along the member length. There were three approaches to determine the flexural stiffness: a deemed to comply minimum member thickness technique and two analytical approached which were Branson’s method for bending stiffness and Bischoff’s method for bending stiffness that directly determined an effective moment of inertia.Branson (1977) developed a deflection calculation technique based on the effective moment of inertia concept. The formula of effective moment of inertia based on Branson’s method is given byI c=(M cra)3I g+[1−(M cra)3]I crwhere M cr is the cracking moment; M a is the maximum characteristic moment under the load being considered; I g is the moment of inertia of the gross section; I cr is the cracked moment of inertia.In 1981, Grossman stated that the deflection could be approximately 20% error compared with experiment results by using Branson’s method. Therefore, Branson’s method was simplified by Grossman such that I cr was no longer required. Other researchers created a new model to show reasonable results and estimate the deflection of reinforced concrete members. They found that it was significantly more accurate than Branson’s model even this model was not accurate when applied to heavy loads.Bischoff (2005) developed an alternative formulation for effective moment of inertia. The formula of effective moment of inertia based on Bischoff’s method is given byI c=I cr1−[1−I crI g](M crM a )2He pointed out that Branson`s approach consistently underestimate short-term deflection of lightly reinforced concrete members. In Branson’s equation, the member stiffness was7overestimated when flexure members had an I gratio greater than 3 and reinforcing ratio lessI crthan 1%.Figure 2.1 illustrated the relationship between the maximum L/h ratio andρfor simply supported members subjected to a uniformly distributed load according to Branson’s method and Bischoff’s method. The results showed that maximum span to depth ratios should decrease as the span length increased, as the design load increases or as the cracking moment decreases. ArrayFigure 2.4. Variation in maximum span to depth ratio based on longitudinal reinforcementratio (Tang et al, 2008)When slender floor slabs are used, the serviceability criteria are not being adequatelyaddressed. Slabs are thin, planar, horizontal, flexural members that are used as floors inbuildings. Because a slab is thin in relation to its span dimensions, the major problem to be8considered in serviceability design is crack and deflection. In 1994, Terezia and Jan discussed the relationship between deflection and the different levels of long term loading of one way slabs including those when cracking occur. Three series of slabs were tested subjected to different levels of loading in 800 days. A linear relationship between initial and time dependent deflection could be showed in their experiments while heavy loading acting on the slabs. It concluded that the deflection surfaces of two way slabs at two certain time intervals were similar regardless of intensive crack development. And the ratio of final deflection to the initial deflection depended on the age of concrete at the time of load acting.2.3 Reinforced concrete beamReinforced concrete beams are widely used in the floor systems construction as the main structural elements in flexure. In the design of reinforced concrete beam, a designer must also satisfy strength and serviceability to prevent deflection and cracking of beam.In 2009, Kara et al had investigated effect of loading types and reinforcement ratio on an effective moment of inertia and deflection of a reinforced concrete beam. Different models for the effective moment of inertia which included the effect of cracking and participation of tensile concrete between cracks had been used to define the effective flexural behaviour of reinforced concrete beam cracked section in their research. Ba sed on Bronson’s studies, the effective moment of inertia is given by:I eff=(M crM )m I1+[1−(M crM)m]I2, for M≥M cr I eff=I1, for M<M crWhere I1and I2are the moments of inertia of the gross uncracked section which accounts for the reinforcing steel to the stiffness, and the cracked transformed section, respectively, M is the bending moment, M cr is the moment corresponding to flexural cracking considered.In Kara’s study, the effective moment of inertia of a cracked member ha d also effected on the probability based effective stiffness model which considered the cracking of concrete with the stiffness reduction in the reinforced concrete flexural members. Crack member in the9reinforced concrete structures needed to be identified and their effective flexural and shear determined in order to find out the accurate deflection. The effect of concrete cracking on the stiffness of a flexural member was largely dependent on both the magnitude and shape of the moment diagram, which was related to the type of applied loading.In 2001, Gilbert illustrated that the simplified procedures for calculation deflection were developed from tests on simply supported reinforced concrete beams. In his article, it is basically wrong to calculate the deflection induced by shrinkage by multiplying the load induced short term deflection by a long term deflection multiplier. The reason was that the creep and shrinkage characteristics of concrete and the age at first loading were neglected. So he developed a more reliable simple model to get reasonable results. In his model, the deflection could be obtained by double integration when loading and shrinkage caused curvatures.Stewart (1996) performed a study on serviceability reliability of reinforced concrete beams. The instantaneous creep and shrinkage deflection and probabilities of serviceability failure for reinforced concrete beams was estimated using his model. It was found that the probabilities of serviceability failure increase with time. It increased as the beam span increased as well. A relative large proportion of long term deflection occurred in the first year and remaining deflection occurred in the next 10 years. The deflection also was affected by variability of the concrete compressive strengths, dead and live loads, modelling errors and relative humidity.10Chapter 3 MethodologyThe behaviour of reinforced concrete floor systems have been designed and analysed in the project. The major components which are slabs and beams will be discussed to these reinforced concrete floor systems. Three different reinforced concrete floor systems which are one way slab, two way slab and flat slab floor systems are designed taking into consideration of strength and serviceability conditions. All the detailed of design procedures are showed in the appendix.This section describes in detail the various aspect of concrete design procedure that is designed by AS3600-2009. Various notations used in this section are listed in the below. SI units can be used for input.3.1. Notations (List of Symbols Used in the AS 3600-2009 Code)A sc Area of compression reinforcement, mm2A st Area of tension reinforcement, mm2a Depth of compression block, mma max Maximum allowed depth of compression block, mmb Width of member, mmb ef Effective width of flange (flanged section), mmb w Width of web (flanged section), mmc Depth to neutral axis, mmd’ Concrete cover to compression reinforcement, mmd Distance from compression face to tension reinforcement, mmdo distance of the extreme compression fibre of the concrete to the centroid11of the outermost layer of tensile reinforcement,mmD Overall depth of a section, mmD s Thickness of slab (flanged section), mmE c Modulus of elasticity of concrete, MPaE s Modulus of elasticity of reinforcement, MPaf′c Specified compressive strength of concrete, Mpaf y yield strength of flexural reinforcement, MPaf c Stress in the compression reinforcement, MPaK u Ratio of the depth to the neutral axis from the compression face, to the effective depth, d (neutral axis parameter)M* the bending moment at the cross section due to the design load for the strength limit state , N-mmγFactor for obtaining depth of compression block in concreteεc Strain in concreteεs Strain in reinforcement∅Strength reduction factor∆/L ef Deflection ratio limitL ef The effective span (mm)k3= 1 for one way slab=0.95 for a two way flat slab without drop panels=1.05 for a flab slab with drop panels12k4=1.6 for simply supported slabs=2 in an end span= 2.4 in interior spansF d.ef= the effective design load, per unit area, taken as(a) (1+k cs)g+(ψs +k csψl)q for total deflection(b) k cs g+(ψs +k csψl)q for the deflection that occurs after the addition orattachment of the partitionsψs ,ψlform AS/NZS1170.03.2 Combinations of ActionsThe design load combinations which are the various combinations of the load cases for the ultimate limit states used in checking stability. For AS 3600-09, if a structure is subjected to dead load (G), live load (Q). The following load combinations may need to be defined (AS 1170):1.35G (AS/NZS 1170, 4.2.2(a))1.2G + 1.5Q (AS/NZS 1170, 4.2.2(b))If roof live load is treated separately or other types of loads are present, other appropriate load combinations should be used. For this project, only dead load and live load will be used in the design procedure.3.3 Limits on Material StrengthThe upper and lower limits of f′c are 100 MPa and 20 MPa, respectively, for all floor systems (AS 6.1.1.1(b)). The upper limit of f sy is 500 MPa for all floor system types (AS6.2.1, Table 6.2.1). The code allows use of f′c and f sy beyond the given limits, provided13special care is taken regarding the detailing and ductility (AS 6.1.1, 6.2.1, 19.2.1.1). In this project, the design will not beyond the limit. The different slabs are designed and analysed by changing the value of f′c and f sy.3.4 Strength Safety FactorsThe strength safety factor, φ, is defined as given in AS 2.3(c), Table 2.3:φ = 0.80 for flexureφ = 0.70 for shear3.5 Beam Design ProcedureIn the design of reinforced concrete beams, the required areas of reinforcement is calculated based on the design moments, design load combination, and other criteria described in the project that follows. Beams are designed for major direction only. Effects resulting from any axial forces and minor direction bending that may exist in the beams must be investigated independently. The procedure of beam design will be discussed in the following steps3.5.1 Design Flexural ReinforcementThe beam top and bottom flexural reinforcement is designed at each stage along the beam. In designing the flexural reinforcement for the major moment of a particular beam, the following steps are involved.3.5.1.1 Determine Bending MomentIn the design of flexural reinforcement of reinforced concrete beams, the design moments for each load combination at a particular beam are obtained by factoring the corresponding moments for different load cases with the corresponding load factors.The beam is then designed for the maximum positive and maximum negative design moments obtained from all of the load combinations. Calculation of bottom reinforcement is based on14。