ๅฐŠๆ•ฌ็š„ ๅพฎไฟกๆฑ‡็Ž‡๏ผš1ๅ†† โ‰ˆ 0.046239 ๅ…ƒ ๆ”ฏไป˜ๅฎๆฑ‡็Ž‡๏ผš1ๅ†† โ‰ˆ 0.04633ๅ…ƒ [้€€ๅ‡บ็™ปๅฝ•]
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Design of One-Way Slab

โ€ข
โ€ข
Mohotasimur Anik
Mohotasimur Anik

This document provides details on the design of a continuous one-way reinforced concrete slab. It includes minimum thickness requirements, equations for calculating moments and shear, maximum reinforcement ratios, and minimum reinforcement ratios. An example is then provided to demonstrate the design process. The slab is designed to have a thickness of 6 inches with 0.39 in2/ft of tension reinforcement in the negative moment region and 0.33 in2/ft in the positive moment region.

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DESIGN OF REINFORCED CONCRETE STRUCTURE ONE WAY SLAB Presented by - MD. Mohotasimur Rahman (Anik) 24th batch, AUST
INTROCDUCTION ๏ƒ˜Slab in which the deflected surface is predominantly cylindrical termed as one-way slabs spanning in the direction of curvature. Curvatures, and consequently bending moments, of this slab shall be assumed same for all strips spanning in the shorted direction or in the direction of predominant curvature, the slab being designed to resist flexural stress in that direction only.1 2 ๏ƒ˜If a slab is supported on two opposite sides only, it will bent or deflect in a direction perpendicular to the supported edge. The structure is one way, and the loads are carried by the slab in the deflected short direction (fig-2a).2 If the slab is supported on four sides and the ration of the long side to the short side is equal to or greater than 2, most of the load (about 95% or more) is carried in the short direction, and one- way action is considered for all practical purposes (fig-2b).2 Figure 1. Deflection of One-Way Slab
3 Figure 2. One-way slab
DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜One-way slab may be treated as a beam. A unit strip of slab, usually 1 ft. (or 1 m) at right angles to the supporting girders, is considered a rectangular beam.3 ๏ƒ˜One-way slabs shall be designed to have adequate stiffness to limit deflections or any deformations that affect strength or serviceability of a structure adversely.4 ๏ƒ˜Minimum thickness stipulated in the table 1, shall apply for one-way slabs not supporting or attached to partitions or other construction likely to be damaged by large deflection, unless computation of deflection indicates that a lesser thickness can be used without adverse effects.4 ๏ƒ˜The total slab thickness (ํ‘•) is usually rounded to the next higher 14 inch (5mm). For slab up to thickness 6 inch. Thickness and next higher 0.5 inch. (or 10 mm) for thicker slabs.5 ๏ƒ˜Concrete cover in slabs shall not be less than 34 inch.6 (20 mm) at surface surfaces not exposed to weather or ground. In this case, ํ‘‘=ํ‘• โˆ’34 โˆ’(ํ‘•ํ‘Žํ‘™ํ‘“ ํ‘ํ‘Žํ‘Ÿ ํ‘‘ํ‘–ํ‘Žํ‘šํ‘’ํ‘กํ‘’ํ‘Ÿ).Where, ํ‘‘ is defined as distance from extreme compression fiber to centriod of tension reinforcement.7 ๏ƒ˜Factored moment and shears in one way slab can be found either by elastic analysis or through the use of the same coefficients stated ACI 8.3.3. printed in table 2.8 4
Table 1: Minimum Thickness of Non-Prestressed One-Way Slab (Normal weight concrete and Grade 60 (Grade 420) Reinforcement)ํŸ— Member Minimum thickness, h Simply supported One end continuous Both end continuous cantilever Solid one-way slab ํ‘™ 20 ํ‘™ 24 ํ‘™ 28 ํ‘™ 10 Ribbed one-way slabs ํ‘™ 16 ํ‘™ 18.5 ํ‘™ 21 ํ‘™ 8 Note: (1)For ํ‘“ํ‘ฆ other than 60,000 ํ‘ํ‘ ํ‘– () multiplied tabulated value by 0.4+(ํ‘“ํ‘ฆ100,000) [for ํ‘“ํ‘ฆ other than 420 ํ‘ํ‘šํ‘š2 multiplied tabulated value by 0.4+(ํ‘“ํ‘ฆ700) ] (2)For structural light weight concrete, multiply tabulated values by (1.65โˆ’0.005ํ‘คํ‘) but not less than 1.09. where ํ‘คํ‘ is range in 90 ํ‘กํ‘œ 115 ํ‘™ํ‘ํ‘“ํ‘ก3 .[For structural light weight concrete, multiply tabulated values by (1.65โˆ’0.003ํ‘คํ‘) but not less than 1.09. where ํ‘คํ‘ is range in 1440 ํ‘กํ‘œ 1840 ํ‘˜ํ‘”ํ‘š3 .] DESIGN OF ONE-WAY SOLID SLABS 5
6 DESIGN OF ONE-WAY SOLID SLABS Table:2 Approximate Moments and Shears in Continuous Beams.ํŸํŸŽ Positive moment End span Discontinuous end unrestrained ํ‘คํ‘ขํ‘™ํ‘› 211 Discontinuous end integral with support ํ‘คํ‘ขํ‘™ํ‘› 214 Interior span ํ‘คํ‘ขํ‘™ํ‘› 216 Negative moments at exterior face of first interior support Two spans ํ‘คํ‘ขํ‘™ํ‘› 29 More than two spans ํ‘คํ‘ขํ‘™ํ‘› 210 Negative moment at other faces of interior supports ํ‘คํ‘ขํ‘™ํ‘› 211 Negative moment at face of all supports for (1) Slabs with spans not exceeding 10 ft. and (2) beams where ratio of sum of column stiffness to beam stiffness exceeds eight at each end of the span. ํ‘คํ‘ขํ‘™ํ‘› 212 Continued
7 DESIGN OF ONE-WAY SOLID SLABS Negative moment at interior face of exterior support for members built integrally with supports Where support is spandrel beam ํ‘คํ‘ขํ‘™ํ‘› 224 Where support is a column ํ‘คํ‘ขํ‘™ํ‘› 216 Shear in end members at face of first interior support 1.15 ํ‘คํ‘ขํ‘™ํ‘›2 Shear at face of all other supports ํ‘คํ‘ขํ‘™ํ‘›2 Where , ํ‘คํ‘ข=ํ‘ขํ‘›ํ‘–ํ‘“ํ‘œํ‘Ÿํ‘šํ‘™ํ‘ฆ ํ‘‘ํ‘–ํ‘ ํ‘กํ‘Ÿํ‘–ํ‘ํ‘ขํ‘กํ‘’ํ‘‘ ํ‘™ํ‘œํ‘Žํ‘‘ ; ํ‘™ํ‘›=ํ‘ ํ‘ํ‘Žํ‘› ํ‘™ํ‘’ํ‘›ํ‘”ํ‘กํ‘• โ€ขIf the slab rests freely on its supports the span length may be taken equal to the clear span plus depth of the slab but did not exceed the distance between centers of supports.11 โ€ขIn analysis of frames or continuous construction for determination of moments, span length shall be taken as the distance center-to-center of supports.11 โ€ขIt shall be permitted to analyze solid or ribbed slabs built integrally with supports, with clear spans not more than 10ft, as continuous slabs on knife edge supports with spans equal to the clear spans of the slab and width of beams otherwise neglected.11
8 DESIGN OF ONE-WAY SOLID SLABS Figure 4: Summary of ACI Moment Coefficient: (a) beams with more than two span (b) beams with two spans only (c) slabs with spans not exceeding 10 ft. (d) beams in which the sum of column stiffness exceeds 8 times the sum of beam stiffness at each end of span.ํŸํŸ
9 DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜The conditions under which the moment coefficients for continuous beam and slabs given in table 2 should be used can be summarized as follows:10 โ€ขSpans are approximately equal, with the larger of two adjacent spans not greater than the shorter by more than 20 percent. โ€ขThere are two or more spans. โ€ขLoads are uniformly distributed. โ€ขUnit live load does not exceed three times unit dead load. โ€ขMembers are prismatic. ๏ƒ˜The maximum reinforcement ratio, ํœŒํ‘šํ‘Žํ‘ฅ=0.85ํ›ฝ1 ํ‘“โ€ฒ ํ‘ ํ‘“ํ‘ฆ ํœ–ํ‘ข ํœ–ํ‘ข:ํœ–ํ‘ก ; where, โˆˆํ‘ก= 0.004 a minimum set tensile strain at the nominal member subjected to axial loads less than 0.10ํ‘“โ€ฒ ํ‘ํดํ‘” where ํดํ‘” is the gross area of the cross section, provides the maximum reinforcement ratio.13 and ํœ–ํ‘ข=Maximum usable strain at extreme concrete compression fiber shall be assumed equal to 0.003.14 ๏ƒ˜The minimum required effective depth ํ‘‘ํ‘Ÿํ‘’ํ‘ž= ํ‘€ํ‘ข โˆ…ํœŒํ‘šํ‘Žํ‘ฅํ‘“ํ‘ฆํ‘(1;0.59ํœŒํ‘šํ‘Žํ‘ฅ ํ‘“ํ‘ฆ ํ‘“โ€ฒ ํ‘ ) ;15 ๏ƒ˜Check ํ‘‘>ํ‘‘ํ‘Ÿํ‘’ํ‘ž; (okay) .15 Figure 5. distance from extreme compression fiber to centriod of tension reinforcement
10 DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜Reinforcement, ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 ; where, ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ ; at first assumed, ํ‘Ž=1 to calculate ํดํ‘ ; that value can be substituted in equation of ํ‘Ž to get a better estimate of ํ‘Ž and hence a new ํ‘‘โˆ’ํ‘Ž2 can be determined.16 ๏ƒ˜For structural slabs of uniform thickness the minimum area of tensile reinforcement, ํดํ‘ ํ‘šํ‘–ํ‘› in the direction of the span shall be the same as temperature and shrinkage reinforcement area.17 In no case is the reinforcement ration to be less than 0.0014 .18 Table 3: Minimum Ratios of Temperature and Shrinkage Reinforcement in Slab based on Gross Area.ํŸํŸ– Slabs where Grade 40 (275) or 50 (350) deformed bars are used 0.0020 Slabs where Grade 60 (420) deformed bars or welded wire fabric (plain or deformed) are used 0.0018 Slabs where reinforcement with yield stress exceeding 60,000 psi (420 MPa) measured at a yield strain of 0.35 percent is used 0.0018 ร—60,000 ํ‘“ํ‘ฆ ๏ƒ˜In slabs, primary flexural reinforcement shall be spaced not farther apart than three times slab thickness, nor 18 inch (450 mm).19 and Shrinkage and temperature reinforcement shall be spaced not farther apart than five times the slab thickness, nor 18 in.18
11 ๏ƒ˜Check shear requirements. Determine ํ‘‰ํ‘ข at the distance from ํ‘‘ and calculate โˆ…ํ‘‰ํ‘= 2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘. If 12โˆ…ํ‘‰ํ‘>ํ‘‰ํ‘ข the shear is adequate.20 Note that the provision of minimum area of shear reinforcement where ํ‘‰ํ‘ข exceeds 12โˆ…ํ‘‰ํ‘ does not apply to slabs .21 If ํ‘‰ํ‘ข> 12โˆ…ํ‘‰ํ‘ , it is a common practice to increase the depth of slab .22 so ํ‘‘ can be determine, assuming ํ‘‰ํ‘ข=โˆ…ํ‘‰ํ‘=2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘.23 ๏ƒ˜Straight-bar systems may be used in both tops and bottom of continuous slabs. An alternative bar system of straight and bent (trussed) bars placed alternately may also be used.7 ๏ƒ˜The choice of bar diameter and detailing depends mainly on the steel areas, spacing requirements, and development length.24 DESIGN OF ONE-WAY SOLID SLABS Figure 6. Reinforcement Details in Continuous One-Way Slab: (A) Straight Bars And (B) Bent Bars.ํŸํŸ’
12 QUESTION: The cross-section of a continuous one-way slab in a building is shown in figure 7. The slab are supported by beams that span 12 ft. between simple supports. The dead load on the slab due to self-weight plus 77psf; the live load psf. Design the continuous slab and draw a detailed section. Given ํ‘“โ€ฒ ํ‘=3 ํ‘˜ํ‘ ํ‘– and ํ‘“ํ‘ฆ=40 ํ‘˜ํ‘ ํ‘– Figure 7. Continuous One-Way Slab SOLUTION: Minimum depth, ํ‘•ํ‘šํ‘–ํ‘›=max ํฟ 30= 15ร—1230=6", ํฟ 10= 5ร—1210=6"=6" Dead load = 612ร—0.15+0.077 ํ‘˜ํ‘ ํ‘“=0.152 ํ‘˜ํ‘ ํ‘“ Live load = 0.13 ํ‘˜ํ‘ ํ‘“ Load, ํ‘ค=1.4 ํทํฟ+1.7 ํฟํฟ=0.434 ํ‘˜ํ‘ ํ‘“ Moment โˆ’ํ‘€ํ‘ข=maxโˆ’ ํ‘คํ‘™212,โˆ’ ํ‘คํ‘™212,(โˆ’ ํ‘คํ‘™22)=maxโˆ’8.13 ,โˆ’8.13,โˆ’5.42=โˆ’8.13 ํ‘˜โ€ฒ/ํ‘“ํ‘ก Moment +ํ‘€ํ‘ข=max+ ํ‘คํ‘™214=max +6.975=+6.975 ํ‘˜โ€ฒ/ํ‘“ํ‘ก EXAMPLE OF ONE-WAY SOLID SLABS
13 EXAMPLE OF ONE-WAY SOLID SLABS SFD BMD
14 EXAMPLE OF ONE-WAY SOLID SLABS To maintain โˆ…=0.9, reinforcement ratio corresponding to ํœ€ํ‘ก=0.004 will be selected. ํœŒํ‘šํ‘Žํ‘ฅ=0.85ํ›ฝ1 ํ‘“โ€ฒ ํ‘ ํ‘“ํ‘ฆ ํœ–ํ‘ข ํœ–ํ‘ข+ํœ–ํ‘ก =0.85 ร—0.85ร—360ร—0.0030.003+0.004=0.0155 ํ‘‘ํ‘Ÿํ‘’ํ‘ž= ํ‘€ํ‘ข โˆ…ํœŒํ‘šํ‘Žํ‘ฅํ‘“ํ‘ฆํ‘(1;0.59ํœŒํ‘šํ‘Žํ‘ฅ ํ‘“ํ‘ฆ ํ‘“โ€ฒ ํ‘ ) = 8.13 ร—120.9ร—0.0155ร—60ร—12(1;0.59ร—0.0155ร—603) =3.45"< ํ‘‘ํ‘ํ‘Ÿํ‘œํ‘ฃํ‘–ํ‘‘ํ‘’ํ‘‘=6โˆ’1"=5" (okay) โˆ’ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 = 8.13 ร—120.9ร—60ร—5;0.752 =0.39ํ‘–ํ‘›2ํ‘“ํ‘ก (ํ‘Žํ‘ ํ‘ ํ‘ขํ‘šํ‘–ํ‘›ํ‘” ํ‘Ž=1) ; ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ = 0.39ร—600.85ร—3ร—12=0.76ํ‘–ํ‘› +ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 = 6.975 ร—120.9ร—60ร—5;0.642 =0.33ํ‘–ํ‘›2ํ‘“ํ‘ก ; ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ = 0.38ร—600.85ร—3ร—12=0.65 ํ‘–ํ‘› Minimum Reinforcement ํดํ‘ ํ‘šํ‘–ํ‘›=0.0018 ร—12ร—5=0.11ํ‘–ํ‘›2ํ‘“ํ‘ก ; ํดํ‘ = โˆ’0.39 ํ‘–ํ‘›2ํ‘“ํ‘ก (controls) +0.33 ํ‘–ํ‘›2ํ‘“ํ‘ก (controls) ) Check ํœŒ= ํดํ‘  ํ‘ํ‘‘ = 0.3912ร—5=0.0065>ํœŒํ‘šํ‘Žํ‘ฅ; so โˆ…=0.9 (okay); At ํ‘‘ distance ํ‘‰ํ‘ข= ํ‘คํ‘™ 2โˆ’ํ‘คํ‘‘= 0.434ร—152โˆ’0.434ร—5=1.085 ํ‘˜ํ‘–ํ‘ 12โˆ…ํ‘‰ํ‘= 12ร—2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘=0.85ร—3000ร—12ร—51000=2.79 ํ‘˜ํ‘–ํ‘>ํ‘‰ํ‘ข ( so the provided depth is okay). Use โˆ…12 ํ‘šํ‘š @ 5"ํ‘/ํ‘ at two supports, โˆ…12 ํ‘šํ‘š @ 6"ํ‘/ํ‘ at mid span and โˆ…10 ํ‘šํ‘š @ 12"ํ‘/ํ‘ for temperature and shrinkage reinforcement.
1.BNBC-1993; pg. 6-146. 2.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 300 3.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 302 4.BNBC-1993; pg. 6-155. 5.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 416 6.ACI 318-95; SECTION 7.7.1;pg. 318R318-68 7.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 304 8.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 395 9.NOTE ON ACI 318-08 BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE 10th ed.; pg. 10-2 10.BNBC 1993; pg. 6-147 11.ACI 318-95; SECTION 8.7.4; pg.318/318R-82~83 12.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 396 13.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 81 14.ACI 318-11; SECTION 10.3.5.; pg. 138 15.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 418 16.BNBC-1993; pg. 6-148. 17.BNBC-2011; pg. 6-26. 18.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 417 19.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 416 20.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 308 21.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 310 22.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 262 23.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 424 24.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 305 REFERENCE 15

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Design of One-Way Slab

  • 1. DESIGN OF REINFORCED CONCRETE STRUCTURE ONE WAY SLAB Presented by - MD. Mohotasimur Rahman (Anik) 24th batch, AUST
  • 2. INTROCDUCTION ๏ƒ˜Slab in which the deflected surface is predominantly cylindrical termed as one-way slabs spanning in the direction of curvature. Curvatures, and consequently bending moments, of this slab shall be assumed same for all strips spanning in the shorted direction or in the direction of predominant curvature, the slab being designed to resist flexural stress in that direction only.1 2 ๏ƒ˜If a slab is supported on two opposite sides only, it will bent or deflect in a direction perpendicular to the supported edge. The structure is one way, and the loads are carried by the slab in the deflected short direction (fig-2a).2 If the slab is supported on four sides and the ration of the long side to the short side is equal to or greater than 2, most of the load (about 95% or more) is carried in the short direction, and one- way action is considered for all practical purposes (fig-2b).2 Figure 1. Deflection of One-Way Slab
  • 3. 3 Figure 2. One-way slab
  • 4. DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜One-way slab may be treated as a beam. A unit strip of slab, usually 1 ft. (or 1 m) at right angles to the supporting girders, is considered a rectangular beam.3 ๏ƒ˜One-way slabs shall be designed to have adequate stiffness to limit deflections or any deformations that affect strength or serviceability of a structure adversely.4 ๏ƒ˜Minimum thickness stipulated in the table 1, shall apply for one-way slabs not supporting or attached to partitions or other construction likely to be damaged by large deflection, unless computation of deflection indicates that a lesser thickness can be used without adverse effects.4 ๏ƒ˜The total slab thickness (ํ‘•) is usually rounded to the next higher 14 inch (5mm). For slab up to thickness 6 inch. Thickness and next higher 0.5 inch. (or 10 mm) for thicker slabs.5 ๏ƒ˜Concrete cover in slabs shall not be less than 34 inch.6 (20 mm) at surface surfaces not exposed to weather or ground. In this case, ํ‘‘=ํ‘• โˆ’34 โˆ’(ํ‘•ํ‘Žํ‘™ํ‘“ ํ‘ํ‘Žํ‘Ÿ ํ‘‘ํ‘–ํ‘Žํ‘šํ‘’ํ‘กํ‘’ํ‘Ÿ).Where, ํ‘‘ is defined as distance from extreme compression fiber to centriod of tension reinforcement.7 ๏ƒ˜Factored moment and shears in one way slab can be found either by elastic analysis or through the use of the same coefficients stated ACI 8.3.3. printed in table 2.8 4
  • 5. Table 1: Minimum Thickness of Non-Prestressed One-Way Slab (Normal weight concrete and Grade 60 (Grade 420) Reinforcement)ํŸ— Member Minimum thickness, h Simply supported One end continuous Both end continuous cantilever Solid one-way slab ํ‘™ 20 ํ‘™ 24 ํ‘™ 28 ํ‘™ 10 Ribbed one-way slabs ํ‘™ 16 ํ‘™ 18.5 ํ‘™ 21 ํ‘™ 8 Note: (1)For ํ‘“ํ‘ฆ other than 60,000 ํ‘ํ‘ ํ‘– () multiplied tabulated value by 0.4+(ํ‘“ํ‘ฆ100,000) [for ํ‘“ํ‘ฆ other than 420 ํ‘ํ‘šํ‘š2 multiplied tabulated value by 0.4+(ํ‘“ํ‘ฆ700) ] (2)For structural light weight concrete, multiply tabulated values by (1.65โˆ’0.005ํ‘คํ‘) but not less than 1.09. where ํ‘คํ‘ is range in 90 ํ‘กํ‘œ 115 ํ‘™ํ‘ํ‘“ํ‘ก3 .[For structural light weight concrete, multiply tabulated values by (1.65โˆ’0.003ํ‘คํ‘) but not less than 1.09. where ํ‘คํ‘ is range in 1440 ํ‘กํ‘œ 1840 ํ‘˜ํ‘”ํ‘š3 .] DESIGN OF ONE-WAY SOLID SLABS 5
  • 6. 6 DESIGN OF ONE-WAY SOLID SLABS Table:2 Approximate Moments and Shears in Continuous Beams.ํŸํŸŽ Positive moment End span Discontinuous end unrestrained ํ‘คํ‘ขํ‘™ํ‘› 211 Discontinuous end integral with support ํ‘คํ‘ขํ‘™ํ‘› 214 Interior span ํ‘คํ‘ขํ‘™ํ‘› 216 Negative moments at exterior face of first interior support Two spans ํ‘คํ‘ขํ‘™ํ‘› 29 More than two spans ํ‘คํ‘ขํ‘™ํ‘› 210 Negative moment at other faces of interior supports ํ‘คํ‘ขํ‘™ํ‘› 211 Negative moment at face of all supports for (1) Slabs with spans not exceeding 10 ft. and (2) beams where ratio of sum of column stiffness to beam stiffness exceeds eight at each end of the span. ํ‘คํ‘ขํ‘™ํ‘› 212 Continued
  • 7. 7 DESIGN OF ONE-WAY SOLID SLABS Negative moment at interior face of exterior support for members built integrally with supports Where support is spandrel beam ํ‘คํ‘ขํ‘™ํ‘› 224 Where support is a column ํ‘คํ‘ขํ‘™ํ‘› 216 Shear in end members at face of first interior support 1.15 ํ‘คํ‘ขํ‘™ํ‘›2 Shear at face of all other supports ํ‘คํ‘ขํ‘™ํ‘›2 Where , ํ‘คํ‘ข=ํ‘ขํ‘›ํ‘–ํ‘“ํ‘œํ‘Ÿํ‘šํ‘™ํ‘ฆ ํ‘‘ํ‘–ํ‘ ํ‘กํ‘Ÿํ‘–ํ‘ํ‘ขํ‘กํ‘’ํ‘‘ ํ‘™ํ‘œํ‘Žํ‘‘ ; ํ‘™ํ‘›=ํ‘ ํ‘ํ‘Žํ‘› ํ‘™ํ‘’ํ‘›ํ‘”ํ‘กํ‘• โ€ขIf the slab rests freely on its supports the span length may be taken equal to the clear span plus depth of the slab but did not exceed the distance between centers of supports.11 โ€ขIn analysis of frames or continuous construction for determination of moments, span length shall be taken as the distance center-to-center of supports.11 โ€ขIt shall be permitted to analyze solid or ribbed slabs built integrally with supports, with clear spans not more than 10ft, as continuous slabs on knife edge supports with spans equal to the clear spans of the slab and width of beams otherwise neglected.11
  • 8. 8 DESIGN OF ONE-WAY SOLID SLABS Figure 4: Summary of ACI Moment Coefficient: (a) beams with more than two span (b) beams with two spans only (c) slabs with spans not exceeding 10 ft. (d) beams in which the sum of column stiffness exceeds 8 times the sum of beam stiffness at each end of span.ํŸํŸ
  • 9. 9 DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜The conditions under which the moment coefficients for continuous beam and slabs given in table 2 should be used can be summarized as follows:10 โ€ขSpans are approximately equal, with the larger of two adjacent spans not greater than the shorter by more than 20 percent. โ€ขThere are two or more spans. โ€ขLoads are uniformly distributed. โ€ขUnit live load does not exceed three times unit dead load. โ€ขMembers are prismatic. ๏ƒ˜The maximum reinforcement ratio, ํœŒํ‘šํ‘Žํ‘ฅ=0.85ํ›ฝ1 ํ‘“โ€ฒ ํ‘ ํ‘“ํ‘ฆ ํœ–ํ‘ข ํœ–ํ‘ข:ํœ–ํ‘ก ; where, โˆˆํ‘ก= 0.004 a minimum set tensile strain at the nominal member subjected to axial loads less than 0.10ํ‘“โ€ฒ ํ‘ํดํ‘” where ํดํ‘” is the gross area of the cross section, provides the maximum reinforcement ratio.13 and ํœ–ํ‘ข=Maximum usable strain at extreme concrete compression fiber shall be assumed equal to 0.003.14 ๏ƒ˜The minimum required effective depth ํ‘‘ํ‘Ÿํ‘’ํ‘ž= ํ‘€ํ‘ข โˆ…ํœŒํ‘šํ‘Žํ‘ฅํ‘“ํ‘ฆํ‘(1;0.59ํœŒํ‘šํ‘Žํ‘ฅ ํ‘“ํ‘ฆ ํ‘“โ€ฒ ํ‘ ) ;15 ๏ƒ˜Check ํ‘‘>ํ‘‘ํ‘Ÿํ‘’ํ‘ž; (okay) .15 Figure 5. distance from extreme compression fiber to centriod of tension reinforcement
  • 10. 10 DESIGN OF ONE-WAY SOLID SLABS ๏ƒ˜Reinforcement, ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 ; where, ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ ; at first assumed, ํ‘Ž=1 to calculate ํดํ‘ ; that value can be substituted in equation of ํ‘Ž to get a better estimate of ํ‘Ž and hence a new ํ‘‘โˆ’ํ‘Ž2 can be determined.16 ๏ƒ˜For structural slabs of uniform thickness the minimum area of tensile reinforcement, ํดํ‘ ํ‘šํ‘–ํ‘› in the direction of the span shall be the same as temperature and shrinkage reinforcement area.17 In no case is the reinforcement ration to be less than 0.0014 .18 Table 3: Minimum Ratios of Temperature and Shrinkage Reinforcement in Slab based on Gross Area.ํŸํŸ– Slabs where Grade 40 (275) or 50 (350) deformed bars are used 0.0020 Slabs where Grade 60 (420) deformed bars or welded wire fabric (plain or deformed) are used 0.0018 Slabs where reinforcement with yield stress exceeding 60,000 psi (420 MPa) measured at a yield strain of 0.35 percent is used 0.0018 ร—60,000 ํ‘“ํ‘ฆ ๏ƒ˜In slabs, primary flexural reinforcement shall be spaced not farther apart than three times slab thickness, nor 18 inch (450 mm).19 and Shrinkage and temperature reinforcement shall be spaced not farther apart than five times the slab thickness, nor 18 in.18
  • 11. 11 ๏ƒ˜Check shear requirements. Determine ํ‘‰ํ‘ข at the distance from ํ‘‘ and calculate โˆ…ํ‘‰ํ‘= 2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘. If 12โˆ…ํ‘‰ํ‘>ํ‘‰ํ‘ข the shear is adequate.20 Note that the provision of minimum area of shear reinforcement where ํ‘‰ํ‘ข exceeds 12โˆ…ํ‘‰ํ‘ does not apply to slabs .21 If ํ‘‰ํ‘ข> 12โˆ…ํ‘‰ํ‘ , it is a common practice to increase the depth of slab .22 so ํ‘‘ can be determine, assuming ํ‘‰ํ‘ข=โˆ…ํ‘‰ํ‘=2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘.23 ๏ƒ˜Straight-bar systems may be used in both tops and bottom of continuous slabs. An alternative bar system of straight and bent (trussed) bars placed alternately may also be used.7 ๏ƒ˜The choice of bar diameter and detailing depends mainly on the steel areas, spacing requirements, and development length.24 DESIGN OF ONE-WAY SOLID SLABS Figure 6. Reinforcement Details in Continuous One-Way Slab: (A) Straight Bars And (B) Bent Bars.ํŸํŸ’
  • 12. 12 QUESTION: The cross-section of a continuous one-way slab in a building is shown in figure 7. The slab are supported by beams that span 12 ft. between simple supports. The dead load on the slab due to self-weight plus 77psf; the live load psf. Design the continuous slab and draw a detailed section. Given ํ‘“โ€ฒ ํ‘=3 ํ‘˜ํ‘ ํ‘– and ํ‘“ํ‘ฆ=40 ํ‘˜ํ‘ ํ‘– Figure 7. Continuous One-Way Slab SOLUTION: Minimum depth, ํ‘•ํ‘šํ‘–ํ‘›=max ํฟ 30= 15ร—1230=6", ํฟ 10= 5ร—1210=6"=6" Dead load = 612ร—0.15+0.077 ํ‘˜ํ‘ ํ‘“=0.152 ํ‘˜ํ‘ ํ‘“ Live load = 0.13 ํ‘˜ํ‘ ํ‘“ Load, ํ‘ค=1.4 ํทํฟ+1.7 ํฟํฟ=0.434 ํ‘˜ํ‘ ํ‘“ Moment โˆ’ํ‘€ํ‘ข=maxโˆ’ ํ‘คํ‘™212,โˆ’ ํ‘คํ‘™212,(โˆ’ ํ‘คํ‘™22)=maxโˆ’8.13 ,โˆ’8.13,โˆ’5.42=โˆ’8.13 ํ‘˜โ€ฒ/ํ‘“ํ‘ก Moment +ํ‘€ํ‘ข=max+ ํ‘คํ‘™214=max +6.975=+6.975 ํ‘˜โ€ฒ/ํ‘“ํ‘ก EXAMPLE OF ONE-WAY SOLID SLABS
  • 13. 13 EXAMPLE OF ONE-WAY SOLID SLABS SFD BMD
  • 14. 14 EXAMPLE OF ONE-WAY SOLID SLABS To maintain โˆ…=0.9, reinforcement ratio corresponding to ํœ€ํ‘ก=0.004 will be selected. ํœŒํ‘šํ‘Žํ‘ฅ=0.85ํ›ฝ1 ํ‘“โ€ฒ ํ‘ ํ‘“ํ‘ฆ ํœ–ํ‘ข ํœ–ํ‘ข+ํœ–ํ‘ก =0.85 ร—0.85ร—360ร—0.0030.003+0.004=0.0155 ํ‘‘ํ‘Ÿํ‘’ํ‘ž= ํ‘€ํ‘ข โˆ…ํœŒํ‘šํ‘Žํ‘ฅํ‘“ํ‘ฆํ‘(1;0.59ํœŒํ‘šํ‘Žํ‘ฅ ํ‘“ํ‘ฆ ํ‘“โ€ฒ ํ‘ ) = 8.13 ร—120.9ร—0.0155ร—60ร—12(1;0.59ร—0.0155ร—603) =3.45"< ํ‘‘ํ‘ํ‘Ÿํ‘œํ‘ฃํ‘–ํ‘‘ํ‘’ํ‘‘=6โˆ’1"=5" (okay) โˆ’ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 = 8.13 ร—120.9ร—60ร—5;0.752 =0.39ํ‘–ํ‘›2ํ‘“ํ‘ก (ํ‘Žํ‘ ํ‘ ํ‘ขํ‘šํ‘–ํ‘›ํ‘” ํ‘Ž=1) ; ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ = 0.39ร—600.85ร—3ร—12=0.76ํ‘–ํ‘› +ํดํ‘ = ํ‘€ํ‘ข โˆ…ํ‘“ํ‘ฆํ‘‘;ํ‘Ž2 = 6.975 ร—120.9ร—60ร—5;0.642 =0.33ํ‘–ํ‘›2ํ‘“ํ‘ก ; ํ‘Ž= ํดํ‘ ํ‘“ํ‘ฆ 0.85ํ‘“โ€ฒ ํ‘ ํ‘ = 0.38ร—600.85ร—3ร—12=0.65 ํ‘–ํ‘› Minimum Reinforcement ํดํ‘ ํ‘šํ‘–ํ‘›=0.0018 ร—12ร—5=0.11ํ‘–ํ‘›2ํ‘“ํ‘ก ; ํดํ‘ = โˆ’0.39 ํ‘–ํ‘›2ํ‘“ํ‘ก (controls) +0.33 ํ‘–ํ‘›2ํ‘“ํ‘ก (controls) ) Check ํœŒ= ํดํ‘  ํ‘ํ‘‘ = 0.3912ร—5=0.0065>ํœŒํ‘šํ‘Žํ‘ฅ; so โˆ…=0.9 (okay); At ํ‘‘ distance ํ‘‰ํ‘ข= ํ‘คํ‘™ 2โˆ’ํ‘คํ‘‘= 0.434ร—152โˆ’0.434ร—5=1.085 ํ‘˜ํ‘–ํ‘ 12โˆ…ํ‘‰ํ‘= 12ร—2โˆ…ํ‘“โ€ฒ ํ‘ํ‘ํ‘‘=0.85ร—3000ร—12ร—51000=2.79 ํ‘˜ํ‘–ํ‘>ํ‘‰ํ‘ข ( so the provided depth is okay). Use โˆ…12 ํ‘šํ‘š @ 5"ํ‘/ํ‘ at two supports, โˆ…12 ํ‘šํ‘š @ 6"ํ‘/ํ‘ at mid span and โˆ…10 ํ‘šํ‘š @ 12"ํ‘/ํ‘ for temperature and shrinkage reinforcement.
  • 15. 1.BNBC-1993; pg. 6-146. 2.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 300 3.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 302 4.BNBC-1993; pg. 6-155. 5.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 416 6.ACI 318-95; SECTION 7.7.1;pg. 318R318-68 7.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 304 8.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 395 9.NOTE ON ACI 318-08 BUILDING CODE REQUIREMENTS FOR STRUCTURAL CONCRETE 10th ed.; pg. 10-2 10.BNBC 1993; pg. 6-147 11.ACI 318-95; SECTION 8.7.4; pg.318/318R-82~83 12.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 396 13.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 81 14.ACI 318-11; SECTION 10.3.5.; pg. 138 15.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 418 16.BNBC-1993; pg. 6-148. 17.BNBC-2011; pg. 6-26. 18.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 417 19.DESIGN OF CONCRETE STRENGTHS 13TH EDITION; ARTHUR H. NILSON; pg. 416 20.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 308 21.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 310 22.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 262 23.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 424 24.STRUCTURAL CONCRETE: THEORY & DESIGN 5th ed.; M. NADIM HASSOUN; pg. 305 REFERENCE 15
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