One-Way Wide Module (Skip) Joist Concrete Floor System Design
One-Way Wide Module (Skip) Joist Concrete Floor System DesignA typical floor plan of a 5-story office building is shown below. Wide-module joists, or “skip” joists, are similar tostandard one-way joists, except the pans are 53 in. or 66 in. wide. For the 53 in. pans, the pan depth varies from 16 in.to 24 in., and for 66 in. pans, the range is 14 in. to 24 in. Wide-module systems are economical for long spans withheavy loads and improved vibration resistance (see references). The gravity loads treatment is shown in this exampleand the lateral load effects are resisted by reinforced concrete shear walls. The design procedures shown in ACI 31814 are illustrated in detail in this example. The hand solution is also used for a detailed comparison with the analysisand design results of the engineering software program spBeam.Figure 1 – One-Way Wide Module Joist Concrete Floor Framing SystemVersion: Jan-26-2017
Scope1. Preliminary Sizing .11.1. Preliminary slab thickness and joist dimensions . 11.2. Preliminary column sizes .32. Design of Structural Members .72.1. One-Way Slab Design .72.1.1. Determination of span loads .82.1.2. Determination of design moment and shear .82.1.3. Flexural Design .92.1.4. Shear Design . 122.1.5. Deflections . 122.1.6. Computer Program Solution . 132.1.7. Summary and Comparison of Results . 212.1.8. Conclusions and Observations . 222.2. One-Way Joist Design . 232.2.1. Determination of span loads . 232.2.2. Determination of design moment and shear . 242.2.3. Flexural Design . 252.2.4. Shear Design . 282.2.5. Deflections . 302.2.6. Computer Program Solution . 302.2.7. Summary and Comparison of Results . 392.2.8. Conclusions and Observations . 402.3. Design of Beam along Grid B (Interior Frame) . 412.3.1. Determination of span loads . 422.3.2. Determination of design moment and shear . 432.3.3. Flexural Design . 442.3.4. Shear Design . 472.3.5. Deflections . 482.3.6. Computer Program Solution . 482.3.7. Summary and Comparison of Results . 572.3.8. Conclusions and Observations . 582.4. Design of Beam along Grid A (Exterior Frame) . 592.4.1. Determination of span loads . 612.4.2. Determination of design flexural moment, shear, and torsional moment . 622.4.3. Flexural, Shear, and Torsion Design . 632.4.4. Deflections . 71Version: Jan-26-2017
2.4.5. Computer Program Solution . 712.4.6. Summary and Comparison of Results . 802.4.7. Conclusions and Observations . 812.5. Design of Interior, Edge, and Corner Columns . 832.5.1. Determination of factored loads . 832.5.2. Column Capacity Diagram (Axial-Moment Interaction). 85Version: Jan-26-2017
CodeBuilding Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14)Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10)International Code Council, 2012 International Building Code, Washington, D.C., 2012ReferencesNotes on ACI 318-11 Building Code Requirements for Structural Concrete, Twelfth Edition, 2013 PortlandCement Association.Concrete Floor Systems (Guide to Estimating and Economizing), Second Edition, 2002 David A. FanellaSimplified Design of Reinforced Concrete Buildings, Fourth Edition, 2011 Mahmoud E. Kamara and LawrenceC. NovakDesign DataFloor-to-Floor Height 12 ft (provided by architectural drawings)wc 150 pcffc’ 5,000 psify 60,000 psi (For flexural reinforcement)fyt 60,000 psi (For shear and torsional reinforcement)Superimposed dead load, SDL 20 psf framed partitions, wood studs plaster 2 sidesASCE/SEI 7-10 (Table C3-1)Typical Floor Level, Live load, Lo 80 psf (Office building)ASCE/SEI 7-10 (Table 4-1)Roof Live Load, Lo 20 psf (Ordinary flat roofs)ASCE/SEI 7-10 (Table 4-1)Required fire resistance rating 2 hoursSolution1.Preliminary Sizing1.1. Preliminary slab thickness and joist dimensionsIn this example deflection will be calculated and checked to satisfy project deflection limits. Minimummember thickness and depths from ACI 318-14 will be used for preliminary sizing.a. One-way SlabUsing minimum thickness for solid one-way slabs in Table 7.3.1.1 for the solid slab spanning between the ribs.End Spans:h l72 3.0 in24 24ACI 318-14 (Table 7.3.1.1)1
Interior Spans:h l72 2.6 in28 28ACI 318-14 (Table 7.3.1.1)The minimum slab thickness for wide-module joists for 2-hour fire rating is 4.6 in.IBC 2012 (Table 720.1(3))Therefore, select a slab thickness of 5 in. for all spans.b. One-way JoistThe wide-module joist systems do not meet the limitations of ACI 318-14, 9.8.1.1 through 9.8.1.4. Therefore,the structural members of this type of joist construction shall be designed with standard provisions for slabs andbeams.ACI 318-14 (9.8.1.8)Using minimum thickness for non-prestressed beams in Table 9.3.1.1. For the ribs (part of the joists) supportingthe solid slab.End Span:lh 18.5Interior Span:h l21 384 20.8 in (governs)ACI 318-14 (Table 9.3.1.1)18.5384 18.3 inACI 318-14 (Table 9.3.1.1)21Therefore, select rib depth of 16 in. for a total joist depth of 21 in.Figure 2 – Slab and Joist Dimensions2
1.2. Preliminary column sizesa. Interior ColumnsSelect a preliminary size based on the axial load demand. Determine interior column loads as follows:The governing load combination: U 1.2 D 1.6 L 0.5LrACI 318-14 (Eq. 5.3.1b)Where:D Dead Load; L Live Load; Lr Roof Live LoadTypical Floor Level Loads# of Floors 4Dead Loads, DSelf-weight of wide-module joist system (see Figure 2):Joist average thickness 2 A1 A2 3 4.33 16 5 72 2 6.629 in. 0.5524 ft2 Total Width72Weight of the joist 0.5524 x 150 pcf 82.83 psf.Superimposed dead load 20 psfLive Load, L: Calculate the live load reduction per ASCE/SEI 7-10 K LL AT 15L Lo 0.25 ASCE/SEI 7-10 (Eq. 4-1)Where:L reduced design live load per ft2 of area supported by the memberLo unreduced design live load per ft2 of area supported by the member 80 psfKLL live load element factorASCE/SEI 7-10 (Table 4-2)AT tributary area (30' 0" 32' 0" ) 960 ft2L 80 (0.25 154 960) 39.4 psfWhich satisfies 0.40 Lo requirement for members supporting two or more floors.ASCE/SEI 7-10 (4.7.2)Roof Level LoadsDead Loads, DSelf-weight of wide-module joist system (see Figure 2):Joist average thickness 2 A1 A2 3 4.33 16 5 72 2 6.629 in. 0.5524 ft2 Total Width72Weight of the joist 0.5524 x 150 pcf 82.83 psf.No superimposed dead load at the roofRoof Live Load, Lr: Calculate the roof live load reduction3
Lr Lo R1 R2 ;12 Lr 20ASCE/SEI 7-10 (Eq 4-2)Where:Lo 20 psfR1 0.6 since AT 960 ft2 600 ft2R2 1 for flat roofLr 20 0.6 1.0 12 psfTotal Factored Load on 1st story interior column (@ 1st interior support)Total Floor Load 4 1.2 (82.83 20) 1.6 39.6 960 717,143 lb 717.1 kipsTotal Roof Load 1.2 82.83 1.6 12 960 113,852 lb 113.9 kipsAssume 24 in square column with 4 – # 11 vertical bars with design axial strength, Pn , max of Pn,max 0.80 0.85 f 'c Ag Ast f y Ast ACI 318-14 (22.4.2) Pn,max 0.80 0.65 0.85 5000 24 24 4 1.56 60000 4 1.56 1,453,858 lb Pn,max 1,454 kips 24 24 Column Self-weight 1.2 0.15 5 12 43.2 kips144 Total Reaction @ 1st interior support 1.15 717.1 113.9 43.2 999 kips 1454 kips.Therefore, the preliminary interior column size of 24 in. x 24 in. is adequate.b. Edge (Exterior) ColumnsSelect a preliminary size based on the axial load demand. Therefore, the load take-down for an edge column isdone as follows:The governing load combination: U 1.2 D 1.6 L 0.5LrACI 318-14 (Eq. 5.3.1b)Typical Floor Level Loads# of Floors 4Dead Loads, DSelf-weight of wide-module joist system (see Figure 2):Weight of the joist 82.83 psf.Superimposed dead load 20 psfLive Load, L: Calculate the live load reduction per ASCE/SEI 7-10 L Lo 0.25 K LL AT 15ASCE/SEI 7-10 (Eq. 4-1)Where:4
L reduced design live load per ft2 of area supported by the memberLo unreduced design live load per ft2 of area supported by the member 80 psfKLL live load element factor 4AT tributary area L 80 (0.25 ASCE/SEI 7-10 (Table 4-2)(30' 0" 32' 0" ) 480 ft22154 480) 47.4 psfWhich satisfies 0.40 Lo requirement for members supporting two or more floors.ASCE/SEI 7-10 (4.7.2)Roof Level LoadsDead Loads, DWeight of the joist 82.83 psf.No superimposed dead load at the roofRoof Live Load, Lr: Calculate the roof live load reductionLr Lo R1 R2 ;12 Lr 20ASCE/SEI 7-10 (Eq 4-2)Where:Lo 20 psfR1 1.2 0.001 AT 1.2 0.001 480 0.72 , since 200 ft2 At 480 ft2 600 ft2R2 1 for flat roofLr 20 0.72 1.0 14.4 psfTotal Factored Load on 1st story edge column (@ 1st interior support)Total Floor Load 4 1.2 (82.83 20) 1.6 47.4 480 382,533 lb 382.5 kipsTotal Roof Load 1.2 82.83 1.6 14.4 480 58,770 lb 58.8 kipsAssume 20 in square column with 4 – # 11 vertical bars with design axial strength, Pn , max of Pn,max 0.80 0.85 f 'c Ag Ast f y Ast ACI 318-14 (22.4.2) Pn, max 0.80 0.65 0.85 5000 20 20 4 1.56 60000 4 1.56 1,064,898 lb Pn, max 1,065 kips 20 20 0.15 5 12 30 kips 144 Column Self-weight 1.2 Total Reaction @ 1st interior support 1.15 382.5 58.8 30 537.5 kips 1,065 kips.Therefore, the preliminary edge column size of 20 in. x 20 in. is adequate.5
c. Corner ColumnsSelect a preliminary size based on the axial load demand. Therefore, the load take-down for a corner column isdone as follows:The governing load combination: U 1.2 D 1.6 L 0.5LrACI 318-14 (Eq. 5.3.1b)Typical Floor Level Loads# of Floors 4Dead Loads, DSelf-weight of wide-module joist system (see Figure 2):Weight of the joist 82.83 psf.Superimposed dead load 20 psfLive Load, L: Calculate the live load reduction per ASCE/SEI 7-10 L Lo 0.25 K LL AT 15ASCE/SEI 7-10 (Eq. 4-1)Where:L reduced design live load per ft2 of area supported by the memberLo unreduced design live load per ft2 of area supported by the member 80 psfKLL live load element factor 4AT tributary area L 80 (0.25 ASCE/SEI 7-10 (Table 4-2)(30' 0" 32' 0" ) 240 ft24154 240) 58.7 psfWhich satisfies 0.40 Lo requirement for members supporting two or more floors.ASCE/SEI 7-10 (4.7.2)Roof Level LoadsDead Loads, DWeight of the joist 82.83 psf.No superimposed dead load at the roofRoof Live Load, Lr: Calculate the roof live load reductionLr Lo R1 R2 ;12 Lr 20ASCE/SEI 7-10 (Eq 4-2)Where:Lo 20 psfR1 1.2 0.001 AT 1.2 0.001 240 0.96 , since 200 ft2 At 240 ft2 600 ft2R2 1 for flat roofLr 20 0.96 1.0 19.2 psfTotal Factored Load on 1st story corner column (@ exterior support)6
Total Floor Load 4 1.2 (82.83 20) 1.6 58.7 240 208,623 lb 208.6 kipsTotal Roof Load 1.2 82.83 1.6 19.2 240 31,228 lb 31.2 kipsAssume 20 in square column with 4 – # 11 vertical bars with design axial strength, Pn , max of Pn,max 0.80 0.85 f 'c Ag Ast f y Ast ACI 318-14 (22.4.2) Pn, max 0.80 0.65 0.85 5000 20 20 4 1.56 60000 4 1.56 1,064,898 lb Pn, max 1,065 kips 20 20 0.15 5 12 30 kips 144 Column Self-weight 1.2 Total Reaction @ exterior support 208.6 31.2 30 269.8 kips 1,065 kips.Therefore, the preliminary edge column size of 20 in. x 20 in. is adequate.2.Design of Structural MembersThe design of the following structural members is performed and compared with results of the engineeringsoftware program spBeam:2.1. One-Way Slab2.2. One-Way Joist2.3. Interior Beam2.4. Exterior Beam2.5. Interior Column2.1. One-Way Slab DesignA unit strip of 1 ft is considered for the design of slab spanning between ribs. Note that ACI 318-14 does notallow live load reduction for one-way slabs.Figure 2.1 – Partial plan view illustrating slab design strip7
Slab design involves the following steps:2.1.1. Determination of span loads2.1.2. Determination of design moments and shears2.1.3. Flexural Design2.1.4. Shear Design2.1.5. Deflections2.1.6. Computer Program Solution2.1.7. Summary and comparison of design results2.1.8. Conclusions and observations2.1.1. Determination of span loadsThe following gravity load combinations are considered:U 1.4 DACI 318-14 (Eq. 5.3.1a) 5 w u 1.4 0.15 0.02 0.116 kips/ft per ft 12 U 1.2D 1.6LACI 318-14 (Eq. 5.3.1b) 5 w u 1.2 0.15 0.02 1.6 0.08 0.227 kips/ft per ft12 Span loads are governed by the second load combination.2.1.2. Determination of design moment and shearThe factored moment and shear can be determined using the simplified method if the requirements aresatisfied:ACI 318-14 (6.5.1) Members are prismatic. Loads are uniformly distributed. L 3D (0.08 kips/ft per ft 3 x 0.0825 kips/ft per ft) There are at least two spans. The longer of two adjacent spans does not exceed the shorter by more than 20 percent.Thus, the approximate coefficients can be used. The factored moments and shears are determined andsummarized in the following tables.ACI 318-14 (Table 6.5.2 and Table 6.5.3)8
Table 2.1.2.1 – One-Way Slab Design Moment ValuesLocationDesign Moment ValueExterior Support Negativewu ln2 24End Spanswu lnMid-spanwu ln2 wu ln2 Support Negativewu ln0.227 5.52 0.49 ft-kips/ft0.227 5.52 0.69 ft-kips/ft102 16Interior Spans 0.29 ft-kips/ft1410Mid-span Positive22414Interior Support Negative0.227 5.50.227 5.52 0.43 ft-kips/ft162 110.227 5.52 0.62 ft-kips/ft11Table 2.1.2.2 – One-Way Slab Design Shear ValuesLocationDesign Shear ValueEnd Span at Face of First Interior Support1.15 wu ln2wu lnAt Face of all other Supports2 1.15 0.227 5.5 0.72 kips/ft2 0.227 5.5 0.62 kips/ft22.1.3. Flexural DesignFor the one-way slab of a wide-module joist system, a single layer of longitudinal reinforcement is provided.The first interior support negative moment governs the design as tabulated in Table 2.1.2.1. Therefore, it isfavorable to place the single layer reinforcement closer to the top fiber of the concrete slab. The requiredreinforcement shall be calculated for the first interior support negative moment first. The requiredreinforcement for the end span positive moment shall also be calculated as the low effective depth due to thereinforcement location may govern the required reinforcement amount. Finally, the required reinforcementfor design shall be checked against the minimum shrinkage and temperature reinforcement requirement perACI 318-14 (24.4.3.2).Calculate the required reinforcement to resist the first interior support negative moment:M u 0.69 ft-kips/ftUse welded wire fabric reinforcement, 6 x 6-W5.5 x W5.5 with 1.5 in. concrete cover. The distance fromextreme compression fiber to the centroid of longitudinal tension reinforcement, d, is calculated below:d 5 1.5 0.264 3.368 in.2To determine the area of steel, assumptions have to be made whether the section is tension or compressioncontrolled, and regarding the distance between the resultant compression and tension forces along the slab9
section (jd). In this example, tension-controlled section will be assumed so the reduction factor is equal to0.
The wide-module joist systems do not meet the limitations of ACI 318-14, 9.8.1.1 through 9.8.1.4. Therefore, the structural members of this type of joist construction shall be designed with standard provisions for slabs and beams. ACI 318-14 (9.8.1.8) Using minimum thickness for non-prestressed beams in Table 9.3.1.1. For the ribs (part of the .
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