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Lecture 33 - Design of Two-Way Floor Slab System April 10, 2001 CVEN 444

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Lecture Goals One-way and two-way slab Slab thickness, h

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Comparison of One-way and Two-way slab behavior One-way slabs carry load in one direction. Two-way slabs carry load in two directions.

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Comparison 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

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Comparison of One-way and Two-way slab behavior Flat slab Two-way slab with beams

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Comparison between a two-way slab verses a one-way slab For flat plates and slabs the column connections can vary between:

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Comparison of One-way and Two-way slab behavior Flat Plate Waffle slab

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Comparison 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.

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Comparison of One-way and Two-way slab behavior Economic Choices Flat Plate suitable span 20 to 25 ft with LL= psf Advantages –Low cost formwork –Exposed flat ceilings –Fast Disadvantages –Low shear capacity –Low Stiffness (notable deflection)

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Comparison of One-way and Two-way slab behavior Economic Choices Flat Slab suitable span 20 to 30 ft with LL= psf Advantages –Low cost formwork –Exposed flat ceilings –Fast Disadvantages –Need more formwork for capital and panels

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Comparison of One-way and Two-way slab behavior Economic Choices Waffle Slab suitable span 30 to 48 ft with LL= psf Advantages –Carries heavy loads –Attractive exposed ceilings –Fast Disadvantages –Formwork with panels is expensive

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Comparison of One-way and Two-way slab behavior Economic Choices One-way Slab on beams suitable span 10 to 20 ft with LL= psf –Can be used for larger spans with relatively higher cost and higher deflections One-way joist floor system is suitable span 20 to 30 ft with LL= psf –Deep ribs, the concrete and steel quantities are relative low –Expensive formwork expected.

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Comparison of One-way and Two-way slab behavior w s =load taken by short direction w l = load taken by long direction A = B Rule of Thumb: For B/A > 2, design as one-way slab

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Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floor Section A-A: Moment per ft width in planks Total Moment

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Two-Way Slab Design Static Equilibrium of Two-Way Slabs Analogy of two-way slab to plank and beam floor Uniform load on each beam Moment in one beam (Sec: B-B)

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Two-Way Slab Design Static Equilibrium of Two-Way Slabs Total Moment in both beams Full 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.

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General 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

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General 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.

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Equivalent Frame Method (EFM) Longitudinal equivalent frame Transverse equivalent frame

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Equivalent Frame Method (EFM) Elevation of the frame Perspective view

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Method 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

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Method 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

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Method 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.

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Column and Middle Strips The slab is broken up into column and middle strips for analysis

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Minimum 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.

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Minimum Slab Thickness for two-way construction (a) For f y in psi. But not less than 5 in.

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Minimum Slab Thickness for two-way construction (b) For f y in psi. But not less than 3.5 in.

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Minimum Slab Thickness for two-way construction (c) For Use the following table

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Minimum Slab Thickness for two-way construction Slabs without interior beams spanning between supports and ratio of long span to short span < 2 See section For slabs with beams spanning between supports on all sides.

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Minimum Slab Thickness for two-way construction The definitions of the terms are: h = Minimum slab thickness without interior beams l n = m = Clear span in the long direction measured face to face of column the ratio of the long to short clear span The average value of for all beams on the sides of the panel.

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Definition of Beam-to-Slab Stiffness Ratio, Accounts for stiffness effect of beams located along slab edge reduces deflections of panel adjacent to beams.

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Definition of Beam-to-Slab Stiffness Ratio, With width bounded laterally by centerline of adjacent panels on each side of the beam.

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Beam and Slab Sections for calculation of

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Definition of beam cross-section Charts may be used to calculate Fig

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Minimum Slab Thickness for two-way construction Slabs without drop panels meeting and , t min = 5 in Slabs with drop panels meeting and , t min = 4 in

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Example A 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 f c = 4 ksi and f y = 60 ksi

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Example The 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 f c = 4 ksi and f y = 60 ksi

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Example The cross-sections are:

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Example The resulting cross section:

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