User guide slab

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User guide slab

  1. 1. CITY UNIVERSITY OF HONG KONGDepartment of Building and Construction
  2. 2. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignAbstractReinforced concrete slabs are used in floors, roofs and walls of buildings and as the decks ofbridges. The floor system of a structure can take many forms such as in-situ solid slab, ribbedslabs or precast units. Slabs may span in one direction or in two directions and they may besupported on monolithic concrete beams, steel beams, walls or directly by the structure’scolumns. In this user guide, some common design methods, general assumptions andconsiderations for one-way slabs and two-way slabs will be introduced. Typical demonstrationswill be shown. It will illustrate the programs with some concrete examples. The basic inputrequirements and output characteristics of programs will be also introduced in this user guide.Table of Content 2.1 Introduction to Slab Systems ....................................................................................... 4 2.1.1 Types of slab................................................................................................ ...... 4 2.1.2 Design Methods ................................ ................................ ................................ . 5 2.1.3 General design considerations and assumptions.................................................. 6 2.1.4 Resistance Moment of Solid Slabs................................................................ ...... 7 2.1.5 Resistance Moment of Solid Slabs................................................................ .... 10 2.1.6 Design algorithm.............................................................................................. 11 2.2 R.C. Slab Systems Design Examples ................................ ................................ .......... 13 2.2.1 Design for One-way Slab ................................ ................................ ................. 14 2.2.2 Design for Two-way Slab................................ ................................ ................. 19 CITY UNIVERSITY OF HONG KONG 2 Department of Building and Construction
  3. 3. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignFiguresFigure 1 - One-way slab on beams and girders ................................ ................................ .......... 7Figure 2 - Design procedure for one-way slab design. ................................ ............................. 11Figure 3 - Design procedures for two-way design................................................................ .... 12Figure 4 - Loading input interface for slab systems design................................. ...................... 15Figure 5 – Choose different location................................ ................................ ........................ 16Figure 6 – Selection of distribution steel reinforcement ........................................................... 16Figure 7 – Selection of tensile steel reinforcement................................ ................................... 17Figure 8 - Results of moment resistance for one-way slab. ................................ ...................... 18Figure 9 - Loading input interface for slab systems design................................. ...................... 20Figure 10 – Choose different connection condition for two-way slab....................................... 21Figure 11 - Selection of distribution steel reinforcement................................ .......................... 22Figure 12 – Selection of tension steel reinforcement of resisting moment 1 ............................. 23Figure 13 – Confirmation of reinforcements in different locations ........................................... 24Figure 14 – View reinforcement for resisting moment in different locations ............................ 25Figure 15 – Calculation of reinforcement for resisting moment 4................................ ............. 26TablesTable 1 – Comparison between one-way and two-way slab ....................................................... 4Table 2 - Ultimate bending moment and shear forces in one-way spanning slab ........................ 7 CITY UNIVERSITY OF HONG KONG 3 Department of Building and Construction
  4. 4. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1 Introduction to Slab Systems2.1.1 Types of slabSlabs are plate elements forming floors and roofs in buildings which normally carry uniformlydistributed loads. Slab may be simply supported or continuous over one or more supports and areclassified according to the method of support as follows: 1. Spanning on way between beams or walls 2. Spanning two ways between the support beams or walls 3. Flat slabs carried on columns and edge beams or walls with no interior beamsSlabs may be solid of uniform thickness or ribbed with ribs running in one or two directions.Slabs with varying depth are generally not used. In this application, one-way and two-way solidslabs are discussed.Determination of slab type depends on the ratio of length of longer side to that of shorter side.The comparison between one-way and two-way slab is shown in Table 1. One-way slab Two-way slab Symbol ly/lx >2 ≤2Distribution of reactions on to supportsTable 1 – Comparison between one-way and two-way slab CITY UNIVERSITY OF HONG KONG 4 Department of Building and Construction
  5. 5. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.2 Design MethodsSlabs may be analyzed using the following methods:-1. Elastic methodsIt covers three techniques. a) Idealization into strips or beams spanning one way or a grid with the strips spanning two ways. b) Elastic plate analysis. c) Finite element analysis. It is the best method for irregularly shaped slabs or slabs with non-uniform loads.2. Method of design coefficientsThe moment and shear coefficients are selected from the code, which have been obtained fromyield line analysis3. Yield line methodThe yield line method is a powerful procedure for the design of slabs. It is an ultimate loadmethod of analysis that is based on plastic yielding of an under-reinforced concrete slab section.For the details of the theory and yield line analysis, please refer to “MacGinley, T.J., and Choo,B.S., Reinforced Concrete: Design Theory and Examples, 2nd edition, E & F N Spon, London,1990.” CITY UNIVERSITY OF HONG KONG 5 Department of Building and Construction
  6. 6. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.3 General design considerations and assumptions1) Uniformly loaded slabsSlabs carrying predominantly uniform load are designed on the assumption that they consist of aseries of rectangular beams 1 m wide spanning between supporting beams or walls.2) Arrangement of loadsAlthough the code states that in principle the slab should be designed to resist the mostunfavorable arrangement of loads, usually it is only necessary to design for the single-load caseof maximum design load on all spans or panels. Design load = 1.4G k + 1.6Q k This is permittedsubject to the following conditions: • The area of each bay exceeds 30 m2. • The ratio of characteristic imposed load to characteristic dead load does not exceed 1.25. • The characteristic imposed load does not exceed 5kN/m2 excluding partitions.3) ShearShear stresses are usually low, except where are heavy concentrated loads. But in my FYP, onlyuniform distributed loads (including dead load and live load) are considered so that there is notany shear reinforcement will be considered.4) Distribution reinforcementThe functions of distribution reinforcement are typing the slab together, distributing non-uniformloads through slabs and taking the possible bending moments in the long span. CITY UNIVERSITY OF HONG KONG 6 Department of Building and Construction
  7. 7. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.4 Resistance Moment of Solid Slabs2.1.4.1 One-way Solid SlabsThe Figure 1 shows the typical one-way slab.Figure 1 - One-way slab on beams and girdersSlabs behave primarily as flexural members and design of the cross-section is similar to beams.Breadth is fixed since a unit value of one meter is normally used in calculations. The designultimate moment and shear force are given in Table 2 here.One important note should be mentioned here is 20% redistribution is allowed when using thetable. End support/slab connection Simple Continuous At first Middle Interior interior interior supports At outer Near middle At outer Near middle support spans support of end span support of end supportMoment 0 0.086FL -0.04FL 0.075FL -0.086FL 0.063FL -0.063FLShear 0.4F -- 0.46F -- 0.6F -- 0.5FNote: F is the total design ultimate load ( 1.4G k + 1.6Qk ) L is the effective spanTable 2 - Ultimate bending moment and shear forces in one-way spanning slab CITY UNIVERSITY OF HONG KONG 7 Department of Building and Construction
  8. 8. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.4.2 Two-way Solid SlabsThe design of two-way slab presents varying degrees of difficulty depending on the boundaryconditions. General, there are two types of two-way slab: • Simply supported slabs • Restrained slabsWhen a slab is supported on all four of its sides it effectively spans in both directions, and it issometimes more economical to design the slab on this basis. The amount of bending in eachdirection will depend on the ratio of the two spans and the conditions of restraint at each support.Moment in each direction of span are generally calculated using coefficients which are tabulatedin the codes of practice. Areas of reinforcement to resist the moments are determinedindependently for each direction of span.2.1.4.2.1 Simply supported slabsA slab simply supported on its four sides will deflect about both axes under load and the cornerswill tend to lift and curl up from the supports, causing torsional moments. When no provisionhas been made to prevent this lifting or to resist the torsion then the moment coefficients( α sx , α sy ) may be used and the maximum moments are given by:m sx = α sx nl x 2 in direction of span l xm sy = α sy nl y in direction of span l y 2Where msx and msy are the moments at mid-span on strips of unit width with spans lx (the lengthof longer side) and ly (the length of shorter side) respectively. And n is the total ultimate load perunit area: n = (1.4G k + 1.6Qk ) CITY UNIVERSITY OF HONG KONG 8 Department of Building and Construction
  9. 9. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignThe value of the moment coefficients are derived from the following equations: ly ly ( )4 ( )2 lx lx α sx = α sy =  ly   ly  81 + ( ) 4  81 + ( ) 4   lx   lx The area of reinforcement in direction l x and l y respectively are m sx m sy Asx = Asy = (per meter width) 0.95 f y z 0.95 f y z2.1.4.2.2 Restrained slab spanning in two directionWhen the slabs have fixity at the supports and reinforcement is added to resist the maximummoments per unit width are given bym sx = β sx nl x in direction of span l x 2m sy = β sy nl y in direction of span l y 2Where β sx and β sy are the moment coefficients and n is the total ultimate load per unit area:n = (1.4G k + 1.6Qk ) .β y = (24 + 2 N d + 1.5 N d )1000 2 Nd is the number of discontinuous edges 2 lγ = {3 − 18 x [ β y + β 1 + β y + β 2 ]} 9 ly γ = β x + β3 + β x + β4Note: β 1 and β 2 take values of 4 / 3β y for continuous edges or zero for discontinuous edges.β 3 and β 4 take values of 4 / 3β x for continuous edges or zero for discontinuous edges. CITY UNIVERSITY OF HONG KONG 9 Department of Building and Construction
  10. 10. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignThe area of reinforcement in direction l x and l y respectively are m sx m sy Asx = Asy = (per meter width) 0.95 f y z 0.95 f y z2.1.5 Resistance Moment of Solid SlabsThe theories and procedures regarding shear reinforcement design of the cross-section aresimilar to beams. It would not repeat here. The maximum shear force per unit width are given byv sx = β sx nl x in direction of span l xv sy = β sy nl y in direction of span l yShear reinforcement ratio: Asv bv (v − v c ) = Sv 0.95 f yvAnd the maximum spacing of stirrups in the direction of span is less that 0.75 times the depth ofthe beam. It makes sure that at least one link intercepts a diagonal crack. The area of shearreinforcement in slabs depends on the value of applied shear stress. For details, please refer toBS8110: Part 1, Table 3.16 (Form and area of shear reinforcements in solid slabs). CITY UNIVERSITY OF HONG KONG 10 Department of Building and Construction
  11. 11. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.6 Design algorithmThis section will focus on the discussion of design algorithm for slab systems design includingdesign for one-way and two-way slab.2.1.6.1 One-way Slab System DesignIn one-way slab design, calculation of steel reinforcement for resisting bending moment is verysimilar to the beam design. In the beam design, shear links arrangement was also considered. Butin one-way slab, we assume that there is no shear link in the slab system. Actually, we still checkthe shear resistance. When the shear stress is larger than the concrete shear resistance, the slabwill fail in shear.Figure 2 - Design procedure for one-way slab design. CITY UNIVERSITY OF HONG KONG 11 Department of Building and Construction
  12. 12. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.1.6.2 Two-way Slab System DesignIn two-way slab analysis, the support condition will affect loading and bending factors. In orderto find the ratio, a database should be set up which contain those values. Computer will find outthe ratio from the database. After the ratio is determined, the calculation is very much similar tothe beam design. So the design procedure will follow the beam design.Figure 3 - Design procedures for two-way design CITY UNIVERSITY OF HONG KONG 12 Department of Building and Construction
  13. 13. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.2 R.C. Slab Systems Design ExamplesThe user guide provides a few typical examples for slab systems design. More concrete exampleswith different slab types, such as one-way and two-way slab, and assumptions are available at:http://bccw.cityu.edu.hk/rc.design/example.asp. The completed list of examples is listed asfollows. R.C. Slab Systems Design Examples Example Assumptions/Situations • One-way spanning solid slab • Continuous slab 1 • Equal spans • Two-way spanning solid slab • Simply supported 2 • No provision to resist torsion at the corners • Two-way spanning solid slab • Restrained edge 3 • Corner portion CITY UNIVERSITY OF HONG KONG 13 Department of Building and Construction
  14. 14. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.2.1 Design for One-way Slab2.2.1.1 InputIn this section, a typical example for one-way slab design is shown. Reader may follow thedetailed procedures.Example 1 A continuous one-way slab has three equal spans of 3.5 meter each. The slab depth is assumed to be 140mm. The loading is as 3.5m followings: Dead load (including self-weight, screed, finish, 10m partitions, ceiling) = 5.2 kN/m2 Imposed load = 3.0 kN/m2 The construction materials are Grade 30 concrete and Grade 460 reinforcement. The conditions of exposure are mild and the cover required is 25mm. Design the reinforcement for the positions of near middle point end span and middle interior span. CITY UNIVERSITY OF HONG KONG 14 Department of Building and Construction
  15. 15. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignDetail Procedures 1. Input basic parameters, such as include loads, sections properties, etc. 2. Chick “Submit” when you finish inputting basic parameters. (See Figure 4) 3. Select different location of slab connection. (See Figure 5) 4. Select an appropriate value of distribution reinforcement. In this example, 223mm2 is chosen. (See Figure 6) 5. Select an appropriate value of tension/compression reinforcement. In this example, 335mm2 of tension reinforcement is chosen. 6. Chick “Submit” when you finish choosing areas of reinforcement. (See Figure 7)In this example, since the dead load includes self-weight, screed, finish, partitions and ceiling,therefore, zero value should be inputted for the density of slab. After entering the designparameters, click the “Submit” button to proceed to the next step – selection of slab connection.Figure 4 - Loading input interface for slab systems design. CITY UNIVERSITY OF HONG KONG 15 Department of Building and Construction
  16. 16. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignFigure 5 – Choose different locationUsers may assign appropriate area of reinforcement by selecting from the table in the “Areas ofgroups of bars” section or defining at the “User Define” section. The required and maximumareas of tension reinforcement are shown at the top of the window as shown in Figure 6. In thisexample, 182mm2 is required and 223mm2 is chosen. After selecting distribution reinforcements,then go to selection of tension / compression reinforcements.Figure 6 – Selection of distribution steel reinforcement CITY UNIVERSITY OF HONG KONG 16 Department of Building and Construction
  17. 17. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignThe required and maximum areas of tension reinforcement are shown at the top of the window asshown in Figure 7. In this example, 243mm2 is required. After selecting reinforcements, thenchick the “Submit” bottom.Figure 7 – Selection of tensile steel reinforcement CITY UNIVERSITY OF HONG KONG 17 Department of Building and Construction
  18. 18. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.2.1.1 OutputThe application will show the results quickly. Numerical result and graphical output can beshown in the output part. The section properties and design loadings are displayed at the top ofreinforcement calculation. The detailed calculations, including K value, tension and compressionreinforcement and checking of shear resistance are also displayed. A typical output is shown inFigure 8.Figure 8 - Results of moment resistance for one-way slab. CITY UNIVERSITY OF HONG KONG 18 Department of Building and Construction
  19. 19. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.2.2 Design for Two-way Slab2.2.2.1 InputIn this section, a typical example for one-way slab design is shown. Reader may follow thedetailed procedures.Example 2 A part floor plan for an office building measuring 6m x 6m. (As shown in the right hand side) It consists of restrained slabs poured monolithically with the edge beams. The slab is 175mm thick and the loading is as 6m follows: Total dead load = 6.2 kN/m2 Imposed load = 2.5 kN/m2 6m Design the corner slab using Grade 35 concrete and Grade 460 steel reinforcement. CITY UNIVERSITY OF HONG KONG 19 Department of Building and Construction
  20. 20. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignDetail Procedures 1. Input basic parameters, such as include loads, sections properties, etc. 2. Chick “Submit” when you finish inputting basic parameters. (See Figure 9) 3. Select different location of slab connection. (See Figure 10) 4. Select an appropriate value of distribution reinforcement. In this example, 223mm2 is chosen. (See Figure 11) 5. Chick “Submit” when you finish choosing areas of reinforcement. 6. Select an appropriate value of tension/compression reinforcement for resisting moment 1 (m1), moment 2 (m2), moment 3 (m3), moment 4 (m4), moment 5 (m5) and moment 6 (m6). (See Figure 12) 7. Chick “Confirm” when you finish choosing areas of reinforcement for different location.In this example, since the dead load includes self-weight, screed, finish, partitions and ceiling,therefore, zero value should be inputted for the density of slab. After entering the designparameters, click the “Submit” button to proceed to the next step – selection of slab connection.Figure 9 - Loading input interface for slab systems design. CITY UNIVERSITY OF HONG KONG 20 Department of Building and Construction
  21. 21. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignThere are two types of two-way slab, which includes: simply supported slab and restrained slabs.When considering restrained slabs, user may need to determine the continuity condition of thefour edges.Figure 10 – Choose different connection condition for two-way slabThere are nine type of panel are considered: • Interior panels • One short edge discontinuous • One long edge discontinuous • Two adjacent edges discontinuous • Two short edges discontinuous • Two long edges discontinuous • Three edges discontinuous (one long edge continuous) • Three edges discontinuous (one short edge continuous) • Four edges discontinuous CITY UNIVERSITY OF HONG KONG 21 Department of Building and Construction
  22. 22. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignSelection of distribution steel reinforcement is shown in Figure 11. In this example, 251mm2 ischosen., and then chick “Submit”.Figure 11 - Selection of distribution steel reinforcement CITY UNIVERSITY OF HONG KONG 22 Department of Building and Construction
  23. 23. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignUsers may assign appropriate area of reinforcement by selecting from the table or defining bythemselves. The required and maximum areas of tension reinforcement are shown at the top ofthe table.Figure 12 – Selection of tension steel reinforcement of resisting moment 1 CITY UNIVERSITY OF HONG KONG 23 Department of Building and Construction
  24. 24. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignSummary will be displayed after selection of steel reinforcement, please chick “Confirm” if thereis no any mistake.Figure 13 – Confirmation of reinforcements in different locations CITY UNIVERSITY OF HONG KONG 24 Department of Building and Construction
  25. 25. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems Design2.2.2.2 OutputAfter selecting reinforcements in different location, designer can view the detailed calculation ofreinforcement in each location. In this case, there are six locations, they are from m1 to m6according to Figure 14.For example, suppose that the user want to view the calculation for resisting moment 4, thanselect “Moment 4” and then chick “View Detailed Calculation”. The detail calculation isdisplayed the page. See Figure 14 and Figure 15.Figure 14 – View reinforcement for resisting moment in different locations CITY UNIVERSITY OF HONG KONG 25 Department of Building and Construction
  26. 26. Web-Based Reinforced Concrete Design (Part II): R.C. Slab Systems DesignFigure 15 – Calculation of reinforcement for resisting moment 4 CITY UNIVERSITY OF HONG KONG 26 Department of Building and Construction

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