Presentation on theme: "Lecture 33 - Design of Two-Way Floor Slab System"— Presentation transcript:
1Lecture 33 - Design of Two-Way Floor Slab System April 10, 2001CVEN 444
2Lecture GoalsOne-way and two-way slabSlab thickness, h
3Comparison of One-way and Two-way slab behavior One-way slabs carry load in one direction.Two-way slabs carry load in two directions.
4Comparison of One-way and Two-way slab behavior One-way and two-way slab action carry load in two directions.One-way slabs: Generally, long side/short side > 1.5
5Comparison of One-way and Two-way slab behavior Two-way slab with beamsFlat slab
6Comparison between a two-way slab verses a one-way slab For flat plates and slabs the column connections can vary between:
7Comparison of One-way and Two-way slab behavior Flat PlateWaffle slab
8Comparison of One-way and Two-way slab behavior The two-way ribbed slab and waffled slab system: General thickness of the slab is 2 to 4 in.
9Comparison of One-way and Two-way slab behavior Economic Choices Flat Plate suitable span 20 to 25 ft with LL= psfAdvantagesLow cost formworkExposed flat ceilingsFastDisadvantagesLow shear capacityLow Stiffness (notable deflection)
10Comparison of One-way and Two-way slab behavior Economic Choices Flat Slab suitable span 20 to 30 ft with LL= psfAdvantagesLow cost formworkExposed flat ceilingsFastDisadvantagesNeed more formwork for capital and panels
11Comparison of One-way and Two-way slab behavior Economic Choices Waffle Slab suitable span 30 to 48 ft with LL= psfAdvantagesCarries heavy loadsAttractive exposed ceilingsFastDisadvantagesFormwork with panels is expensive
12Comparison of One-way and Two-way slab behavior Economic Choices One-way Slab on beams suitable span 10 to 20 ft with LL= psfCan be used for larger spans with relatively higher cost and higher deflectionsOne-way joist floor system is suitable span 20 to 30 ft with LL= psfDeep ribs, the concrete and steel quantities are relative lowExpensive formwork expected.
13Comparison of One-way and Two-way slab behavior ws =load taken by short directionwl = load taken by long directiondA = dBRule of Thumb: For B/A > 2, design as one-way slab
14Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floorSection A-A:Moment per ft width in planksTotal Moment
15Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floorUniform load on each beamMoment in one beam (Sec: B-B)
16Two-Way Slab Design Static Equilibrium of Two-Way Slabs Total Moment in both beamsFull load was transferred east-west by the planks and then was transferred north-south by the beams;The same is true for a two-way slab or any other floor system.
17General Design Concepts (1) Direct Design Method (DDM)Limited to slab systems to uniformly distributed loads and supported on equally spaced columns. Method uses a set of coefficients to determine the design moment at critical sections. Two-way slab system that do not meet the limitations of the ACI Code must be analyzed more accurate procedures
18General Design Concepts (2) Equivalent Frame Method (EFM)A three dimensional building is divided into a series of two-dimensional equivalent frames by cutting the building along lines midway between columns. The resulting frames are considered separately in the longitudinal and transverse directions of the building and treated floor by floor.
20Equivalent Frame Method (EFM) Perspective viewElevation of the frame
21Method of Analysis (1) Elastic Analysis Concrete slab may be treated as an elastic plate. Use Timoshenko’s method of analyzing the structure. Finite element analysis
22Method of Analysis (2) Plastic Analysis The yield method used to determine the limit state of slab by considering the yield lines that occur in the slab as a collapse mechanism.The strip method, where slab is divided into strips and the load on the slab is distributed in two orthogonal directions and the strips are analyzed as beams.The optimal analysis presents methods for minimizing the reinforcement based on plastic analysis
23Method of Analysis (3) Nonlinear analysis Simulates the true load-deformation characteristics of a reinforced concrete slab with finite-element method takes into consideration of nonlinearities of the stress-strain relationship of the individual members.
24Column and Middle Strips The slab is broken up into column and middle strips for analysis
25Minimum Slab Thickness for two-way construction The ACI Code specifies a minimum slab thickness to control deflection. There are three empirical limitations for calculating the slab thickness (h), which are based on experimental research. If these limitations are not met, it will be necessary to compute deflection.
26Minimum Slab Thickness for two-way construction (a) Forfy in psi. But not less than 5 in.
27Minimum Slab Thickness for two-way construction (b) Forfy in psi. But not less than 3.5 in.
28Minimum Slab Thickness for two-way construction (c) ForUse the following table
29Minimum Slab Thickness for two-way construction Slabs without interior beams spanning between supports and ratio of long span to short span < 2See section For slabs with beams spanning between supports on all sides.
30Minimum Slab Thickness for two-way construction The definitions of the terms are:h = Minimum slab thickness without interior beamsln =b =am=Clear span in the long direction measured face to face of columnthe ratio of the long to short clear spanThe average value of a for all beams on the sides of the panel.
31Definition of Beam-to-Slab Stiffness Ratio, a Accounts for stiffness effect of beams located along slab edge reduces deflections of panel adjacent to beams.
32Definition of Beam-to-Slab Stiffness Ratio, a With width bounded laterally by centerline of adjacent panels on each side of the beam.
35Beam and Slab Sections for calculation of a Definition of beam cross-sectionCharts may be used to calculate a Fig
36Minimum Slab Thickness for two-way construction Slabs without drop panels meeting and ,tmin = 5 inSlabs with drop panels meeting and ,tmin = 4 in
37ExampleA flat plate floor system with panels 24 by 20 ft is supported on 20 in. square columns. Determine the minimum slab thickness required for the interior and corner panels. Use fc = 4 ksi and fy = 60 ksi
38ExampleThe floor system consists of solid slabs and beams in two directions supported on 20 in square columns. Determine the minimum slab thickness required for an interior panel. Use fc = 4 ksi and fy = 60 ksi