Chapter 10: Bond, Development Length, Hooks, and Splicing of Reinforcement PDF

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CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner CamScanner ANGELO R. OCASLA 01 ENGR. MARK GIL DELA CRUZ SORIANO 11 CHAPTER 10: BOND, DEVELOPMENT LENGTH, HOOKS, AND SPLICING OF REINFORCEMENT 10.0 NOTATIONS & SYMBOLS: 𝑳𝒅 = development length for tension, mm 𝑳𝒅𝒄 = length for compression, mm 𝑳𝒅𝒉 = development length of standard hook, mm 𝑳𝒔𝒄 = Lap splice for compression, mm 𝑳𝒔𝒕 = Lap splice for tension, mm 𝑳𝒆𝒙𝒕 = straight extension, mm 𝒅𝒃 = nominal diameter of bar, mm 𝒇𝒄 ′ = specified compressive stress of concrete, MPa 𝒇𝒚 = specified yield strength of steel, MPa 𝝀 = modification factor (normal-weight or lightweight) ψ𝑒 = modification factor (epoxy) ψ𝑐 = modification factor (cover) ψ𝑇 = modification factor (confining reinforcement) ψ𝑠 = modification factor (size) ψ𝑡 = modification factor (casting position) 10.1 INTRODUCTION BOND STRESSES A basic assumption made for reinforced concrete design is that there must be absolutely no slippage of the bars in relation to the surrounding concrete. In other words, the steel and the concrete should stick together, or bond, so that they will act as a unit. If there is no bonding between the two materials and if the bars are not anchored at their ends, they will pull loose from the concrete. As a result, the concrete beam will act as an unreinforced member and will be subject to sudden collapse as soon as the concrete cracks. 10.2 DEVELOPMENT LENGTH OF REINFORCEMENT (NSCP 2015 SECTION 425.4) Consider a cantilever beam as shown. It can be seen that both the maximum moment in the beam and the maximum stresses in the tensile bars occur at the face of the support. Theoretically, a small distance back into the support the moment is zero, and thus it would see that reinforcing bars would no longer be required. Obviously if the bars were stopped at the face of the support, the beam would fail. The bar stresses must be transferred to the concrete by bond between the steel and the concrete before the bars can be cut off. In this case the bars must be extended some distance back into the support and out into the beam to anchor them or develop their strength. This distance, called the development length (Ld) It can be defined as the minimum length of embedment of bars that is necessary to permit them to be stressed to their yield point plus some extra distance to ensure member toughness. A similar case can be made for bars in other situations and in other types of beams. ANGELO R. OCASLA 02 ENGR. MARK GIL DELA CRUZ SORIANO 11 10.2.1 DEVELOPMENT OF DEFORMED BARS AND DEFORMED WIRES IN TENSION, 𝑳𝒅 (NSCP 2015 SECTION 425.4.2) 425.4.2.1 Development length 𝑳𝒅 for deformed bars and deformed wires in tension shall be the greater of (a) and (b); a. Length calculated in accordance with Section 425.4.2.2 or 425.4.2.3 using the applicable modification factors of Section 425.4.2.4; b. 300mm 425.4.2.2 For deformed bars or wires, 𝑳𝒅 shall be calculated in accordance with Tab 425.4.2.2. Table 425.4.2.2 Development Length for Deformed Bars and Deformed Wires in Tension 20mmØ and smaller bars 25mmØ and larger Spacing and Cover and deformed wires bars Clear spacing of bars or wires being developed or lap-spliced not less than 𝒅𝒃 clear cover at least 𝒅𝒃 and stirrups or ties throughout 𝑳𝒅 not less than the 𝑓𝑦 ψ𝑡 ψ𝑒 𝑓𝑦 ψ𝑡 ψ𝑒 Code minimum, ( ) 𝒅𝒃 ( ) 𝒅𝒃 or 2.1𝜆√𝑓𝑐 ′ 1.7𝜆√𝑓𝑐 ′ Clear spacing of bars or wires being developed or lap spliced at least 𝟐𝒅𝒃 and clear cover at least 𝒅𝒃 𝑓𝑦 ψ𝑡 ψ𝑒 𝑓𝑦 ψ𝑡 ψ𝑒 Other cases ( ) 𝒅𝒃 ( ) 𝒅𝒃 1.4𝜆√𝑓𝑐 ′ 1.1𝜆√𝑓𝑐 ′ ANGELO R. OCASLA 03 ENGR. MARK GIL DELA CRUZ SORIANO 11 425.4.2.3 For deformed bars or wires, 𝑳𝒅 shall be calculated in accordance with Tab 425.4.2.2. 𝟏 𝒇𝒚 𝛙 𝒕 𝛙𝒆 𝛙𝒔 𝑳𝒅 = ( ) 𝒅𝒃 𝟏. 𝟏 𝝀√𝒇𝒄′ (𝒄𝒃 + 𝑲𝒕𝒓 ) 𝒅𝒃 𝒄𝒃 + 𝑲𝒕𝒓 in which the confinement term( ) shall not exceed 2.5, and 𝒅𝒃 𝟒𝟎𝑨𝒕𝒓 𝑲𝒕𝒓 = 𝒔𝒏 where, n is the number of bars or wires being developed or lap spliced along the plane of splitting. It shall be permitted to use 𝑲𝒕𝒓 = 0 as a design simplification even if transverse reinforcement is present. 𝑲𝒕𝒓 is a factor that represents the contribution of confining reinforcement across potential splitting planes. 𝑨𝒕𝒓 is the total cross-sectional area of all transverse reinforcement within spacing s that crosses the potential plane of splitting through the reinforcement being developed, mm2 𝒄𝒃 is lesser of: (a) the distance from center of a bar or wire to the nearest concrete surface, and (b) one-half the center-to-center spacing of bars or wires being developed, mm 425.4.2.4 For the calculation of 𝑳𝒅 modification factors shall be in accordance with Table 425.4.2.4. ANGELO R. OCASLA 04 ENGR. MARK GIL DELA CRUZ SORIANO 11 Table 425.4.2.4 Modification Factors for Development of Deformed Bars and Deformed Wires in Tension Modification Factor Condition Value of Factor Lightweight concrete 0.75 Lightweight Lightweight concrete, where 𝒇𝒄𝒕 In accordance with 𝝀 is specified Section 419.2.4.3 Normal-weight concrete 1.0 Epoxy-coated or zinc and epoxy dual-coated reinforcement with 1.5 clear cover less than 𝟑𝒅𝒃 or Epoxy clear spacing less than 𝟔𝒅𝒃 Epoxy-coated or zinc and epoxy 𝛙𝒆 dual-coated reinforcement for all 1.2 other conditions Uncoated or zinc-coated 1.0 (galvanized) reinforcement 25mmØ and larger bars 1.0 Size 𝛙𝒔 20mmØ and smaller bars and 0.8 deformed wires More than 300mm of fresh Casting Position concrete placed below 1.3 𝛙𝒕 horizontal reinforcement Other 1.0 The product ψ𝑡 ψ𝑒 need not exceed 1.7 10.2.2 DEVELOPMENT OF STANDARD HOOKS IN TENSION, 𝑳𝒅𝒉 ith (NSCP 2015 SECTION 425.4.3) 425.4.3.1 Development length 𝑳𝒅𝒉 for deformed bars in tension terminating in a standard hook shall be the greater of (a) through (c): 𝒇𝒚 𝛙 𝒆 𝛙 𝒄 𝛙 𝒓 a. ( ) 𝒅𝒃 𝟒.𝟕𝝀√𝒇𝒄′ b. 𝟖𝒅𝒃 c. 150 mm 425.4.3.2 For the calculation of 𝑳𝒅𝒉 modification factors shall be in accordance with Table 425.4.3.2. Factors 𝛙𝒄 and 𝛙𝒓 shall be permitted to be taken as 1.0. At discontinuous ends of members Section 425.4.3.3 shall apply. ANGELO R. OCASLA 05 ENGR. MARK GIL DELA CRUZ SORIANO 11 Table 425.4.3.2 Modification Factors for Development of Hooked Bars in Tension Modification Factor Condition Value of Factor Lightweight concrete 0.75 Lightweight Lightweight concrete, where 𝑓𝑐𝑡 is In accordance with 𝝀 specified Section 419.2.4.3 Normal-weight concrete 1.0 Epoxy-coated or zinc and epoxy 1.2 Epoxy dual-coated reinforcement 𝛙𝒆 Uncoated or zinc-coated (galvanized) 1.0 reinforcement For 36mmØ bar and smaller hooks with side cover (normal to plane of Cover hook) ≥ 65mm and for 90-degree 0.7 𝛙𝒄 hook with cover on bar extension beyond hook ≥ 50mm Other 1.0 For 90-degree hooks of 36mmØ and smaller bars 1. enclosed along 𝑳𝒅𝒉 within ties or stirrups perpendicular to 𝑳𝒅𝒉 at Confining 𝒔 ≤ 𝟑𝒅𝒃 or 0.8 Reinforcement 𝛙𝒓 2. enclosed along the bar extension beyond hook including the bend within ties or stirrups perpendicular to 𝑳𝒆𝒙𝒕 at 𝒔 ≤ 𝟑𝒅𝒃 Other 1.0 1. The first tie or stirrup shall enclose the bent portion of the hook within 𝟐𝒅𝒃 of the outside of the bend. 2. 𝒅𝒃 is the nominal diameter of the hooked bar. ANGELO R. OCASLA 06 ENGR. MARK GIL DELA CRUZ SORIANO 11 425.4.3.3 For bars being developed by a standard hook at discontinuous ends of members with both side cover and top (or bottom) cover over hook less than 65mm, (a) through (c) shall be satisfied: a. The hook shall be enclosed along 𝑳𝒅𝒉 within ties or stirrups perpendicular to 𝑳𝒅𝒉 at s ≤ 3𝒅𝒃 ; b. The first tie or stirrup shall enclose the bent portion of the hook within 2𝒅𝒃 , of the outside of the bend c. 𝛙𝒓 shall be taken as 1.0 in calculating 𝑳𝒅𝒉 in accordance with Section 425.4.3.1(a) where 𝒅𝒃 is the nominal diameter of the hooked bar. 10.2.3 DEVELOPMENT LENGTH OF DEFORMED BARS AND DEFORMED WIRES IN COMPRESSION (NSCP 2015 SECTION 425.4.9) 425.4.9.1 Development length 𝑳𝒅𝒄 for deformed bars and deformed wires in compression shall be the greater of (a) and (b); ANGELO R. OCASLA 07 ENGR. MARK GIL DELA CRUZ SORIANO 11 a. Length calculated in accordance with Section 425.4.9.2 b. 200 mm 425.4.9.2 𝑳𝒅𝒄 shall be the greater of (a) and (b), multiplied by the modification factors of Section 425.4.9.3: 𝟎.𝟐𝟒𝒇𝒚𝛙𝒓 a. ( ) 𝒅𝒃 𝝀√𝒇𝒄′ b. 𝟎. 𝟎𝟒𝟑𝒇𝒚𝛙𝒓 𝒅𝒃 425.4.9.3 For the calculation of 𝑳𝒅𝒄 modification factors shall be in accordance with Table 425.4.9.3, except 𝛙𝒓 shall be permitted to be taken as 1.0 Table 425.4.9.3 Modification Factors for Deformed Bars and Wires in Compression Modification Factor Condition Value of Factor Lightweight concrete 0.75 Lightweight Lightweight concrete, where 𝑓𝑐𝑡 is In accordance with 𝝀 specified Section 419.2.4.3 Normal-weight concrete 1.0 Reinforcement enclosed within (1), (2), (3) or (4); 1. a spiral 2. a circular continuously wound tie 𝐝𝐛 ≥ 6mm and pitch ≤ 100mm Confining 3. 6mm bar or MD130 wire ties in 0.75 Reinforcement 219 accordance with Section 𝛙𝒓 425.7.2 spaced ≤ 100mm on center 4. hoops in accordance with Section 425.7.4 spaced ≤100mm on center Other 1.0 10.2.4 DEVELOPMENT LENGTH OF BUNDLED REINFORCEMENT (NSCP 2015 SECTION 425.6.1.5) 425.6.1.5 Development length for individual bars within a bundle, in tension or compression, shall be that of the individual bar, increased 20 percent for a three-bar bundle, and 33 percent for a four-bar bundle. 10.2.5 REDUCTION OF DEVELOPMENT LENGTH FOR EXCESS REINFORCEMENT (NSCP 2015 SECTION 425.4.10) 425.4.10.1 Reduction of development lengths defined in Sections 425.4.2.1(a), 425.4.3.1(a) and 425.4.9.1(a) shall be permitted by use of the ratio ANGELO R. OCASLA 08 ENGR. MARK GIL DELA CRUZ SORIANO 11 𝐀 𝒔,𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 /𝐀 𝒔,𝒑𝒓𝒐𝒗𝒊𝒅𝒆𝒅 except where prohibited by Section 425.4.10.2. The modified development lengths shall not be less than the respective minimums specified in Sections 425.4.2.1(b), 425.4.3.1(b). 425.4.3.1(c) and 425.4.9.1(b) 425.4.10.2 A reduction of development length in accordance with Section 425.4.10.1 is not permitted for (a) through (e). (a) At the face of non-continuous support; (b) At other locations where anchorage or development for fy is required; (c) Where bars are required to be continuous; (d) For headed and mechanically anchored deformed reinforcement; (e) In seismic-force-resisting systems in structures assigned to Seismic zone 4. 10.3 HOOKS (NSCP 2015 SECTION 425.3) When sufficient space is not available to anchor tension bars by running them straight for their required development lengths as required by the Code, hooks may be used. (Hooks are considered ineffective for compression bars for development length purposes.) 10.3.1 STANDARD HOOKS, SEISMIC HOOKS, CROSS TIES, AND MINIMUM INSIDE BEND DIAMETERS (NSCP 2015 SECTION 425.3) 425.3.1 Standard hooks for the development of deformed bars in tension shall conform to Table 425.3.1 Table 425.3.1 Standard Hook Geometry for Development of Deformed Bars in Tension Minimum Straight Type of inside bend Type of Standard Hook Standard Bar Size extension 𝑳𝒆𝒙𝒕 diameter, Hook mm mm 10mmØ through 25mmØ 6𝑑𝑏 90-degree 28mmØ through 36mmØ 8𝑑𝑏 12𝑑𝑏 hook 40mmØ and 58mmØ 10𝑑𝑏 10mmØ through 25mmØ 6𝑑𝑏 Greater of 𝟒𝒅𝒃 and 180- 65mm 28mmØ degree through 36mmØ 8𝑑𝑏 hook 40mmØ and 58mmØ 10𝑑𝑏 ANGELO R. OCASLA 09 ENGR. MARK GIL DELA CRUZ SORIANO 11 425.3.2 Minimum inside bend diameters for bars used as transverse reinforcement and standard hooks for bars used to anchor stirrups, ties, hoops, and spirals shall conform to Table 425.3.2. Standard hooks shall enclose longitudinal reinforcement. Table 425.3.2 Minimum Inside Bend Diameters and Standard Hook Geometry for Stirrups, Ties, and Hoops Type of Minimum Straight Type of Standard Hook Standard Bar Size inside bend extension Hook diameter, mm 𝑳𝒆𝒙𝒕 mm Greater of 10mmØ through 16mmØ 4𝑑𝑏 𝟒𝒅𝒃 and 75mm 90-degree hook 20mmØ through 25mmØ 6𝑑𝑏 12𝑑𝑏 10mmØ through 16mmØ 4𝑑𝑏 135- Greater of degree 𝟒𝒅𝒃 and hook 75mm 20mmØ through 25mmØ 6𝑑𝑏 10mmØ through 16mmØ 4𝑑𝑏 180- Greater of degree 𝟒𝒅𝒃 and hook 20mmØ 65mm through 25mmØ 6𝑑𝑏 A standard hook for stirrups, ties, and hoops includes the specific bend diameter and straight extension length. It shall be permitted to use a longer straight extension at the end of a hook. A longer extension shall not be considered to increase the anchorage capacity of the hook. 10.4 SPLICES OF REINFORCEMENT/LAP SPLICES (NSCP 2015 SECTION 425.5) Field splices of reinforcing bars are often necessary because of the limited commercial bar lengths available, requirements at construction joints, and changes from larger bars to smaller bars. Splicing may be done by welding, by mechanical connections, or most frequently by lapping bars. Lapped bars are usually tied in contact. 425.5.1.1 Lap splices shall not be permitted for bars larger than 36mm Ø, except as provided in Section 425.5.5.3. 10.4.1 TENSION LAP SPLICE, Lst The NSCP 2015 divides tension lap slices into two different classifications, A and B, depending on the percentage of the bars spliced in a given length and on the reinforcement stress at the splice. Table 425.5.2.1 shows the requirements for both Class A and Class B splices. ANGELO R. OCASLA 10 ENGR. MARK GIL DELA CRUZ SORIANO 11 425.5.2.1 Tension lap splice length Lst for deformed bars and deformed wires in tension shall be in accordance with Table 425.5.2.1, where La shall be in accordance with Section 425.4.2.1 (a). Table 425.5.2.1 Lap Splice Lengths of Deformed Bars and Deformed Wires in Tension Maximum percent 𝑨𝒔,𝒑𝒓𝒐𝒗𝒊𝒅𝒆𝒅 / 𝑨𝒔,𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 of 𝑨𝒔 spliced within Splice Type 𝑳𝒔𝒕 over length of splice required lap length 50 Class A Greater of: 1.0 𝑳𝒅 and ≥ 2.0 100 Class B 300mm Greater of: 1.3 𝑳𝒅 and < 2.0 All cases Class B 300mm Ratio of area of reinforcement provided to area of reinforcement required by analysis at splice location 425.5.2.2 If bars of different size are lap spliced in tension. 𝑳𝒔𝒕 shall be the greater of 𝑳𝒅 of the larger bar and 𝑳𝒔𝒕 of the smaller bar. 10.4.2 COMPRESSION LAP SPLICE 𝑳𝒔𝒕 A compression lap splice, a portion of the force transfer is through the bearing of the end of the bar on the concrete. Reinforcing bars in compression are spliced usually to columns where bars are most often terminated just above each floor or every other floor. The minimum length of lap splice for compression is according to NSCP 2015 Section 425.5.5. LAP SPLICE LENGTHS OF DEFORMED BARS IN COMPRESSION (NSCP 2015 SECTION 425.5.5) 425.5.5.1 Compression lap splice length 𝑳𝒔𝒄 of 36mm Ø or smaller bars in compression shall be calculated in accordance with (a) or (b): a. For fy ≤ 420 MPa: 𝑳𝒔𝒄 is the greater of 𝟎. 𝟎𝟕𝟏𝒇𝒚 𝒅𝒃 and 300mm. b. For fy > 420 MPa: 𝑳𝒔𝒄 is the greater of (0.13𝒇𝒚 -24) 𝒅𝒃 and 300mm. For fc < 21 MPa, the length of lap shall be increased by one-third 425.5.5.2 Compression lap splices shall not be used for bars larger than 36mm Ø, except as permitted in Section 425.5.5.3 425.5.5.3 Compression lap splices of 40mm Ø or 58mm Ø bars to 36mm Ø or smaller bars shall be permitted and shall be in accordance with Section 425.5.5.4. 425.5.5.4 Where bars of different size are lap spliced in compression, 𝑳𝒆 shall be the greater of 𝑳𝒅𝒄 of larger bar calculated in accordance with Section 425 4.9.1 and 𝑳𝒔𝒆 of smaller bar calculated in accordance with Section 425.5.5.1 as appropriate 10.4.3 LAP SPLICE FOR BEAM 418.6.3.3 Lap splices of deformed longitudinal reinforcement shall be permitted if hoop or spiral reinforcement is provided over the lap length. Spacing of the transverse reinforcement enclosing the lap spliced bars shall not exceed the smaller of d/4 and 100mm. Lap splices shall not be used in locations (a) through (c): ANGELO R. OCASLA 11 ENGR. MARK GIL DELA CRUZ SORIANO 11 a. Within the joints; b. Within a distance of twice the beam depth from the face of the joint; c. Within a distance of twice the beam depth from the critical sections where yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior 10.4.4 LAP SPLICE FOR COLUMN 418.7.4.3 Mechanical splices shall conform to Section 418.2.7 and welded splices shall conform to Section 418.2.8. Lap splices shall be permitted only within the center half of the member length, shall be designed as tension lap splices, and shall be enclosed within transverse reinforcement in accordance with Sections 418.7.5.2 and 418.7.5.3. ANGELO R. OCASLA 01 ENGR. MARK GIL DELA CRUZ SORIANO 07 CHAPTER 11: ANALYSIS AND DESIGN OF ONE-WAY SLABS 11.0 NOTATIONS & SYMBOLS: 𝒇𝒄 ′ = specified compressive stress of concrete, MPa 𝒇𝒚 = specified yield strength of steel, MPa 𝒃 = width of compression face of member, mm 𝒅 = distance from extreme compression fiber to centroid of tension reinforcement, mm 𝒉 = total slab thickness, mm 𝒔 = spacing of bar, mm 𝒅𝒃 = diameter of bar, mm 𝒅𝒂𝒈𝒈 = diameter of aggregates, mm 𝑨𝒃𝒂𝒓 = area of bar, mm2 𝑨𝒔 = required area of steel, mm2 𝑨𝒔,𝒎𝒊𝒏 = minimum area of steel, mm2 𝑨𝒈 = gross concrete area, mm2 ⍴ = steel reinforcement ratio ⍴𝒎𝒊𝒏 = minimum steel reinforcement ratio 𝒘𝒖 = factored uniform load, kN/m 𝒘𝑫 = uniform service dead load, kN/m 𝒘𝑳 = uniform service live load, kN/m 11.1 TYPES OF STRUCTURAL SLABS REINFORCED CONCRETE SLAB are large flat plates that are supported by reinforced concrete beams, walls, or columns; by masonry walls; by structural steel beams or columns; or by the ground. If they are supported on two opposite sides only, they are referred to as one-way slabs because the bending is in one direction only - that is, perpendicular to the supported edges. Should the slab be supported by beams on all four edges, it is referred to as a two-way slab because bending is in both directions. Actually, if a rectangular slab is supported ion all four sides, but the long side is two or more times as long as the short side, the slab will, for all practical purposes, act as one-way slabs. 𝑳 If ≥ 𝟐 One way slab 𝑺 𝑳 If < 𝟐 Two way slab 𝑺 where: L = longer span length S = Shorter span length ANGELO R. OCASLA 02 ENGR. MARK GIL DELA CRUZ SORIANO 07 11.2 ANALYSIS AND DESIGN OF ONE-WAY SLABS A one-way slab is considered as a wide, shallow, rectangular beam. The reinforcing steel is usually spaced uniformly over its width. One-way slabs are analyzed by considering a one-meter strip, which is assumed independent of the adjacent strips. This method of analysis is somewhat conservative because we neglected the lateral restraint provided by the adjacent strips. 11.2.1 MINIMUM SLAB THICKNESS (NSCP 2015 SECTION 407.3.1) 407.3.1.1 For solid non-prestressed slabs not supporting or attached to partitions or other construction likely to be damaged by large deflections, overall slab thickness h shall not be less than the limits in Table 407.3.1.1, unless the calculated deflection limits of Section 407.3.2 are satisfied. Table 407.3.1.1 Minimum Thickness of Solid Non-Prestressed One-Way Slabs Support Condition Minimum Simply supported L/20 One end continuous L/24 Both Ends Continuous L/28 Cantilever L/10 Expression applicable for normal weight concrete and fy = 420 MPa. For other cases, minimum h shall be modified in accrodance with Sections 407.3.1.1.1 through 407.3.1.1.3 as appropriate ANGELO R. OCASLA 03 ENGR. MARK GIL DELA CRUZ SORIANO 07 407.3.1.1.1 For fy other than 420 MPa, the expressions in Table 407.3.1.1 shall be multiplied by (0.4+fy/700). 11.2.2 MINIMUM FLEXURAL REINFORCEMENT IN NON-PRESTRESSED SLABS (NSCP 2015 SECTION 407.6.1) 407.6.1.1 A minimum area of flexural reinforcemet 𝑨𝒔,𝒎𝒊𝒏 shall be provided in accordance with Table 407.6.1.1 Table 407.6.1.1 𝑨𝒔,𝒎𝒊𝒏 for Non-Prestressed One-Way Slabs Reinforcement Type 𝒇𝒚 MPa 𝑨𝒔,𝒎𝒊𝒏 Deformed Bars < 420 0.002𝐴𝑔 0.0018(420) 𝐴𝑔 Deformed bars or welded ≥ 420 Greater of: 𝑓𝑦 wire reinforcement 0.0014𝐴𝑔 11.2.3 MINIMUM SHRINKAGE AND TEMPERATURE REINFORCEMENT (NSCP 2015 SECTION 407.6.4) 407.6.4.1 Reinforcement shall be provided to resist shrinkage and temperature stresses in accordance with Section 424.4 424.4.3.2 The ratio of deformed shrinkage and temperature reinforcement area to gross concrete area shall satisfy the limits in Table 424.4.3.2 Table 424.4.3.2 Minimum Ratios of Deformed Shrinkage and Temperature Reinforcement Area to Gross Concrete Area Reinforcement Type 𝒇𝒚 MPa Minimum Reinforcement Ratio Deformed Bars < 420 0.002 0.0018(420) Deformed bars or welded ≥ 420 Greater of: 𝑓𝑦 wire reinforcement 0.0014 424.4.3.3 The spacing of deformed shrinkage and temperature reinforcement shall not exceed the lesser of 5h and 450mm 11.2.4 MINIMUM AND MAXIMUM SPACING OF REINFORCEMENT (NSCP 2015 SECTION 407.7.2) 407.7.2.1 Minimum spacing s for parallel non-prestressed reinforcement in a horizontal layer, clear spacing shall be at least the greatest of 25mm, db, and (4/3)dagg 407.7.2.3 Maximum spacing s of deformed reinforcement shall be the lesser of 3h and 450mm ANGELO R. OCASLA 04 ENGR. MARK GIL DELA CRUZ SORIANO 07 11.3 NSCP COEFFICIENTS FOR CONTINUOUS BEAMS AND ONE-WAY SLABS (NSCP 2015 SECTION 406.5) The NSCP Coefficient Method is a simplified and an approximate method used for the analysis of continuous beams and one-way slab. This method allows the real rotation restraint at external supports where the real moment is not equal to zero. Thus, the coefficient method is more realistic but is only valid when its conditions of application are satisfied in accordance with Section 406.5.1. 406.5.1 It shall be permitted to calculate Mu due to gravity loads in accordance with this section for continuous beams and one-way slabs satisfying (a) through (e): a. Members are prismatic; b. Loads are uniformly distributed; с. L≤3D; d. There are at least two spans; e. The longer of two adjacent spans does not exceed the shorter by 20 percent. 406.5.2 Mu due to gravity loads shall be calculated in accordance with Table 406.5.2 Table 406.5.2 Approximate Moments for Non-Prestressed Continuous Beams and One-Way Slabs Moment Location Condition 𝑴𝒖 Discontinuous end integral 𝑊𝑢 𝐿2𝑛 / 14 with support End span Discontinuous end Positive 𝑊𝑢 𝐿2𝑛 / 11 unrestrained Interior spans All 𝑊𝑢 𝐿2𝑛 / 16 Member built integrally with 𝑊𝑢 𝐿2𝑛 / 24 Interior face of exterior supporting spandrel beam support Member built integrally with 𝑊𝑢 𝐿2𝑛 / 16 supporting column Exterior face of first Two spans 𝑊𝑢 𝐿2𝑛 / 9 interior support More than two spans 𝑊𝑢 𝐿2𝑛 / 10 Positive Face of other supports All 𝑊𝑢 𝐿2𝑛 / 11 a. Slabs with spans not exceeding 3m. b. Beams where ratio of Face of all supports sum of column stiffnesses 𝑊𝑢 𝐿2𝑛 / 12 satisfying (a) or (b) to beam stiffnesses exceeds 8 at each end of span To calculate negative moments, 𝑳𝒏 shall be the average of the adjacent clear span lengths. 406.5.3 Moments calculated in accordance with Section 406.5.2 shall not be redistributed. 406.5.4 Vu due to gravity loads shall be calculated in accordance with Table 406.5.4. ANGELO R. OCASLA 05 ENGR. MARK GIL DELA CRUZ SORIANO 07 Table 406.5.4 Approximate Shears for Non-Prestressed Continuous Beams and One-Way Slabs Location 𝑽𝒖 Exterior face of first interior support 1.15𝑊𝑢 𝐿𝑛 / 12 Face of all other supports 𝑊𝑢 𝐿𝑛 / 12 ANGELO R. OCASLA 06 ENGR. MARK GIL DELA CRUZ SORIANO 07 Note: *The exterior negative moment depends on type of support: If the support is a beam or girder, the coefficient is -1/24 If the support is a column, the coefficient is -1/16 11.4 STEPS IN THE DESIGN OF ONE-WAY SLAB I. Determine the minimum slab thickness h in Table 407.3.1.1. II. Compute the effective depth d 𝟏 𝒅 = 𝒉 − 𝒄𝒐𝒏𝒄𝒓𝒆𝒕𝒆 𝒄𝒐𝒗𝒆𝒓 − 𝒅𝒃 𝟐 III. Compute the Factored Moment M2 to be carried by slab (consider Im width of slab) 𝑾𝒖 = 𝟏. 𝟐𝑾𝑫 + 𝟏. 𝟔𝑾𝑳 IV. Check whether the slab thickness is adequate for the maximum moment. Assume Ø = 0.90 𝟓𝟏 𝟑 𝑴𝒖 = Ø 𝑩𝒇𝒄′ 𝒃𝒅𝟐𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 (𝟏 − 𝑩) 𝟏𝟒𝟎 𝟏𝟒 𝒅𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 = _______ if d ≥ 𝒅𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 , slab thickness is adequate if d < 𝒅𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅. slab thickness is not adequate, increase h V. Compute the required A, per meter width of slab 𝑴𝒖 = Ø 𝑹𝒏 𝒃𝒅𝟐 𝟎. 𝟖𝟓𝐟𝐜′ 𝟐𝑹𝒏 𝝆= (𝟏 − √𝟏 − ) 𝐟𝐲 𝟎. 𝟖𝟓𝐟𝐜′ Check 𝝆𝒎𝒊𝒏 in Table 407.6.1.1 𝑨𝒔 = 𝝆𝐛𝐝 ANGELO R. OCASLA 07 ENGR. MARK GIL DELA CRUZ SORIANO 07 VI. Determine the required main bar spacing 𝑨𝒃𝒂𝒓 𝑺𝒑𝒂𝒄𝒊𝒏𝒈 𝒔 = 𝒙 𝟏𝟎𝟎𝟎 𝑨𝒔 Maximum spacing required by Section 407.7.2.3: Maximum spacing s of deformed reinforcement shall be the lesser of: (a) 3h (b) 450mm VII. Temperature bars: 𝑨𝒔 = 𝝆𝒎𝒊𝒏 𝐛𝐝 𝑨𝒃𝒂𝒓 𝑺𝒑𝒂𝒄𝒊𝒏𝒈 𝒔 = 𝒙 𝟏𝟎𝟎𝟎 𝑨𝒔 Check 𝝆𝒎𝒊𝒏 in Table 424.4.3.2 Maximum spacing required by Section 407.7.2.3: The spacing of deformed shrinkage and temperature reinforcement shall not exceed the lesser of: (a) 5h (b) 450mm