Reinforced Concrete Structures/Design Aids

Transcription

1 AREA OF BARS (mm 2 ) Reinforced Concrete Structures/Design Aids Size of s (mm) Number of s * Available troug special request. MINIMUM BEAM WIDTH (mm) ACCORDING TO THE ACI CODE Size of Bars (mm) Number of s Add for eac added Table sows minimum beam widts wen φ10 stirrups are used. For additional s, add dimension in last column for eac added. For s of different sizes, determine from te table te beam widt for smaller size s and ten add last column figure for eac larger used. Assume maximum aggregate size does not exceed tree-fort of te clear space between s (ACI-3-3.3). Table computation procedure is in agreement wit te ACI code interpretation of te ACI Committee 340. A B C D A = 40 mm clear cover to stirrups B = 10 mm stirrup diameter C = use twice te diameter of φ10 stirrups. D = clear distance between s = d b or 25.4 mm, wicever is greater (were d b is te diameter of te larger adjacent longitudinal ) Dr. Hazim Dwairi/Hasemite University Page 1

2 Development Lengt of Straigt Bars and Standard Hooks For deformed s, ACI Section defines te development lengt ld given in te table below. Note tat ld sall not be less tan 300 mm. Case f20 > f20 Case 1: Clear spacing of s being developed not less tan db, clear cover not less tan db, and stirrups trougout ld not less tan code minimum or Case 2: Clear spacing of s being developed not less tan 2db and clear cover not less tan db l 12 f ψ ψ λ 12 f ψ ψ λ y t e y t e d = db ld = d b ' ' 25 fc 20 f c Oter cases l d 18 f ψ ψ λ 18 f ψ ψ λ y t e y t e = d b ld = d b ' ' 25 f c 20 f c Te terms in te foregoing equations are as follows: ψ t = reinforcement location factor Horizontal reinforcement so placed tat more tan 300 mm of fres concrete is cast in te member below te development lengt Oter reinforcement ψ e = coating factor Epoxy-coated s wit cover less tan 3db, or clear spacing less tan 6db All oter epoxy-coated s Uncoated reinforcement λ = ligtweigt aggregate concrete factor Wen all-ligtweigt aggregate concrete is used Wen sand-ligtweigt aggregate concrete is used Normal weigt concrete is used Dr. Hazim Dwairi/Hasemite University Page 2

3 Table 1: Basic tension development-lengt ratio, l d /d b (mm/mm) ldb ld = ψ eλ d b, but not less tan 300 mm d Bar size (mm) b f c = 21 MPa f c = 25 MPa f c = 28 MPa f c = 30 MPa f c = 35 MPa Bottom Top Bottom Top Bottom Top Bottom Top Bottom Top Case 1: Clear spacing of s being developed not less tan db, clear cover not less tan db, and stirrups trougout ld not less tan code minimum, or Case 2: Clear spacing of s being developed not less tan 2db and clear cover not less tan db f y = 420 MPa, uncoated s, normal weigt concrete f > f f y = 300 MPa, uncoated s, normal weigt concrete f Oter Cases: f > f f y = 300 MPa, uncoated s, normal weigt concrete f For top s, more tan 300 mm of fres concrete is cast in te member (i.e. α = 1.3) β is te coating factor, and λ is te ligtweigt concrete factor Wen tere is insufficient lengt available to develop a straigt, standard ooks are used. Te standard 90 degree ook is sown below: φ10 to φ25: R = 3d b φ28 to φ32: R = 4d b φ28 to φ50: R = 5d b Dr. Hazim Dwairi/Hasemite University Page 3

4 Te development lengt of a ook, l d, is given by te following equation. Note tat te development lengt sall not be less tan 8db nor less tan 150mm: l d 0.24 f yψ = ' f c e λ d b 8db larger of 150mm were ψ e = te coating factor = 1.2 for epoxy coated s and 1.0 for uncoated reinforcement, and λ is te ligtweigt aggregate factor = 1.3 for ligtweigt aggregate concrete. For oter cases ψ e and λ, sall be taken as 1.0 Standard Hooks ACI sections 7.1 and Ld db Ld db R R 2R 12db o 90 Hook 4db or 65 mm o 180 Hook φ10 to φ25: R = 3d b φ28 and φ32: R = 4d b φ50: R = 5d b Stirrups and tie ooks ACI section φ16 and smaller: 6db φ18 to φ25: 12db φ25 and smaller: 6db R R R R Beam C L Beam C L R R o 90 Stirrup Hooks o 135 Stirrup Hooks φ16 & smaller: R = 2d b φ18 to φ25: R = 4d b Dr. Hazim Dwairi/Hasemite University Page 4

5 Requirements for structural integrity in spandrel beams Requirements for structural integrity in interior beams Dr. Hazim Dwairi/Hasemite University Page 5

6 ACI Moment and Sear Coefficients M u = C m (w u l n 2 ) ; C m : moment envelope coefficient V u = C v (w u l n /2) ; C v : sear envelope coefficient Were w u is total factored load and l n is clear span Discontinuous End End Span Interior Spans Interior face of exterior support (a) Terminology Exterior face of first interior support C m = -1/9 if only two spans Oter faces of interior supports C m = C v = 0.0 1/11-1/10-1/11-1/16-1/11-1/ Eq Eq (b) Discontinuous end unrestrained C m = -1/9 if only two spans C m = C v = -1/24 1/14-1/10-1/11 1/16-1/11-1/ Eq Eq (c) Discontinuous end integral wit support were support is spandrel beam C m = -1/9 if only two spans C m = C v = -1/16 1/14-1/10-1/11 1/16-1/11-1/ Eq Eq (d) Discontinuous end integral wit support were support is a column 0.25wLu Eq. 1: C = v l arger of (0.15) or, were w Lu is factored live wu Dr. Hazim Dwairi/Hasemite University Page 6

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8 Instantaneous Deflection Calculations: Δ = 5 48 M a is te support moment for cantilevers and te midspan moment (wen K is so defined) for simple and continuous beams. Long-term Deflection: Δ = (Δ ) = 1+50 ξ = t = 3 monts ξ = t = 6 monts ξ = t = one year ξ = t > 5 years Dr. Hazim Dwairi/Hasemite University Page 8

9 Direct Design Metod (DDM) Two-way Slabs Total Static Moment = M = o w u l 8 l 2 2 n Dr. Hazim Dwairi/Hasemite University Page 9

10 Total static moment distribution Dr. Hazim Dwairi/Hasemite University Page 10

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12 Rectangular Column Interaction Diagrams Dr. Hazim Dwairi/Hasemite University Page 12

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15 Circular Column Interaction Diagrams Dr. Hazim Dwairi/Hasemite University Page 15

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