Example Building. The following example illustrates the

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1 The following example illustrates the design TIME SAVING methods DESIGN presented AIDS in the article Timesaving Design Aids for Reinforced Concrete, Part 2: Two-way Slabs, by David A. Fanella, which appeared in the October 2001 edition of Structural Engineer magazine. Unless otherwise noted, all referenced table, figure, and equation numbers are from that article. Example Building Page 1 of 14 Below is a partial plan of a typical floor in a cast-in-place reinforced concrete building. In this example, an interior strip of a flat plate floor system is designed and detailed The following example illustrates the design methods presented in the PCA book Simplified Design - Reinforced Concrete Buildings of Moderate Size and Height third edition. Unless otherwise noted, all referenced table, figure, and equation numbers are from that book. for the effects of gravity loads according to ACI Example Building Below is a partial plan of a typical floor in a cast-in-place reinforced concrete building. In this example, an interior strip of a flat plate floor system is designed and detailed for the effects of gravity loads according to ACI Design strip x 20 (typ.) 24 x 24 (typ.) Design Data Materials Concrete: normal weight (150 pcf), 3 /4-in. maximum aggregate, f c = 4,000 psi Mild reinforcing steel: Grade 60 (f y = 60,000 psi) Loads Superimposed dead loads = 30 psf Live load = 50 psf

2 TIME SAVING DESIGN AIDS Page 2 of 14 Minimum Slab Thickness Longest clear span l n = 24 (20/12) = ft From Fig. 4-3, minimum thickness h per ACI Table 9.5(c) = l n /30 = 8.9 in. Use Fig. 1-8 to determine h based on shear requirements at interior column assuming a 9 in. slab: q u = 1.2( ) + 1.6(50) = psf A = 24 x 20 = 480 ft 2 A/c 12 = 480/2 2 = 120 From Fig. 1-8, d/c d h = 0.22 x 24 = 5.3 in. = = 6.55 in. Try preliminary h = 9 in. Design for Flexure Use Fig. 4-4 to determine if the Direct Design Method of ACI Sect can be utilized to compute the bending moments due to the gravity loads: 3 continuous spans in one direction, more than 3 in the other O.K. Rectangular panels with long-to-short span ratio = 24/20 = 1.2 < 2 O.K. Successive span lengths in each direction are equal O.K. No offset columns O.K. L/D = 50/( ) = 0.35 < 2 O.K. Slab system has no beams N.A. Since all requirements are satisfied, the Direct Design Method can be used. Total panel moment M o in end span: 2 2 qull 2 n M o = = 8 8 = ft - kips Total panel moment M o in interior span: 2 2 qull 2 n M o = = 8 8 = 244 ft - kips For simplicity, use M o = ft-kips for all spans. Division of the total panel moment M o into negative and positive moments, and then column and middle strip moments, involves the direct application of the moment coefficients in Table 4-2.

3 TIME SAVING DESIGN AIDS Page 3 of 14 Slab Moments End Spans Int. Span (ft-kips) Ext. neg. Positive Int. neg. Positive Total Moment Column Strip Middle Strip Note: All negative moments are at face of support. Required slab reinforcement. M Span Location u b * d ** As Min. As (ft-kips) (in.) (in.) (in. 2 ) (in. 2 ) Reinforcement + End Span Ext. neg No. 4 Column Positive No. 4 Strip Int. Neg No. 4 Ext. neg No. 4 Middle Positive No. 4 Strip Int. Neg No. 4 Interior Span Column Strip Positive No. 4 Middle Strip Positive No. 4 * Column strip width b = (20 x 12)/2 = 120 in. * Middle strip width b = (24 x 12) 120 = 168 in. ** Use average d = = 7.75 in. A s = M u /4d where M u is in ft-kips and d is in inches Min. A s = bh = b; Max. s = 2h = 18 in. or 18 in. (Sect ) + For maximum spacing:120/18 = 6.7 spaces, say 8 bars 168/18 = 9.3 spaces, say 11 bars Design for Shear Check slab shear and flexural strength at edge column due to direct shear and unbalanced moment transfer. Check slab reinforcement at exterior column for moment transfer between slab and column. Portion of total unbalanced moment transferred by flexure = γ f M u b 1 = 20 + (7.75/2) = in. b 2 = = in. b 1 /b 2 = 0.86 From Fig. 4-16, γ f = 0.62 * * The provisions of Sect may be utilized; however, they are not in this example.

4 TIME SAVING DESIGN AIDS Page 4 of 14 γ f M u = 0.62 x 64.6 = 40 ft-kips Required A s = 40/(4 x 7.75) = 1.29 in. 2 Number of No. 4 bars = 1.29/0.2 = 6.5, say 7 bars Must provide 7-No. 4 bars within an effective slab width = 3h + c 2 = (3 x 9) + 20 = 47 in. Provide the required 7-No. 4 bars by concentrating 7 of the column strip bars (11-No. 4) within the 47 in. slab width over the column. Check bar spacing: For 7-No. 4 within 47 in. width: 47/7 = 6.7 in. < 18 in. O.K. For 4-No. 4 within = 73 in. width: 73/4 = in. > 18 in. Add 1 additional bar on each side of the 47 in. strip; the spacing becomes 73/6 = 12.2 in. < 18 in. O.K. Reinforcement details at this location are shown in the figure on the next page. Check the combined shear stress at the inside face of the critical transfer section.

5 TIME SAVING DESIGN AIDS Page 5 of 14 v u = V A u c vm + γ Jc / u Factored shear force at edge column: V u = 0.251[(24 x 10.83) (1.99 x 2.31)] = 64.1 kips When the end span moments are determined from the Direct Design Method, the fraction of unbalanced moment transferred by eccentricity of shear must be 0.3M o = 0.3 x = 74.6 ft-kips (Sect ). γ v = 1 γ f = = 0.38 c 2 /c 1 = 1.0 c 1 /d = 20/7.75 = 2.58 From Table 4.9 A c = (2b 1 + b 2 ) d = in. 2 J c = [2b 1 d(b 1 + 2b 2 ) + d 3 (2b 1 + b 2 )/b 1 ]/6 = 5,141 in. 3 v u = 64, , , 141 v u = = psi Determine allowable shear stress φv c from Fig. 4-13: b o /d = (2b 1 + b 2 )/d b o /d = [(2 x ) ]/7.75 = 9.74 β c = 1 φv c = psi > v u = psi OK 9 slab is OK Reinforcement Details The figures below show the reinforcement details for the column and middle strips. The bar lengths are determined from Fig of ACI

6 TIME SAVING DESIGN AIDS Page 6 of 14 The PCA computer program pcaslab can be used to expedite the design of different slab systems. The program covers wide range of two-way slab systems and can be used for more complex slab layouts. The output of the program for the slab in the example is shown in the following pages. Please note that the Equivalent Frame Method is used by the pcaslab program.

7 TIME SAVING DESIGN AID Page 7 of 14 X Z Y pcaslab v2.00. Licensed to: pcastructurepoint. License ID: D2DE-2C8D0 File: C:\Data\Time Saving Design Aid\.slb Project: Time Saving Design Aids Frame: Two-Way Slab Engineer: PCA

8 TIME SAVING DESIGN AID Page 8 of 14 Middle Strip Flexural Reinforcement 10-#4(81.9) 12-#4(83.9) 11-#4(55.6) 16-#4(240.0)c 11-#4(55.2) 12-#4(83.3) 12-#4(83.3) 11-#4(55.2) 10-#4(240.0)c 11-#4(55.6) 12-#4(83.9) 10-#4(81.9) 16-#4(240.0)c 14-#4(73.4) 14-#4(240.0)c 14-#4(82.5) 14-#4(82.5) 14-#4(240.0)c 14-#4(73.4) 14-#4(240.0)c Column Strip Flexural Reinforcement pcaslab v2.00. Licensed to: pcastructurepoint. License ID: D2DE-2C8D0 File: C:\Data\Time Saving Design Aid\.slb Project: Time Saving Design Aids Frame: Two-Way Slab Engineer: PCA

9 TIME SAVING DESIGN AID Page 9 of Middle Strip Moment Capacity - k-ft Column Strip Moment Capacity - k-ft LEGEND: Envelope Curve Capacity Curve Support Centerline Face of Support pcaslab v2.00. Licensed to: pcastructurepoint. License ID: D2DE-2C8D0 File: C:\Data\Time Saving Design Aid\.slb Project: Time Saving Design Aids Frame: Two-Way Slab Engineer: PCA

10 TIME SAVING DESIGN AID Page 10 of 14 pcaslab v2.00 Portland Cement Association , 11:27:26 AM Licensed to: pcastructurepoint, License ID: D2DE-2C8D0 c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Page 1 ooooooo oooooo ooooo oooooooo oooooooo ooooooo oo oo oo oo oo oo oo oo oo oo oo oooooooo oo ooooooo ooooo ooooooo oo oo ooooooo ooooo oo oo oo oo oo oo oooooooo oo oo oo oooooo oo oo oooooo o o oooooooo oo ooooo oo oo oo o oo oo oooo oo o oo oo oooooo oo oooooo oooooo oooo oo oo oo oo oo oo oo oo oo oo oo oooooooo oo o oo oo oo oo oooooo ooo ooooo o ooooo ============================================================================= pcaslab v2.00 (TM) A Computer Program for Analysis, Design, and Investigation of Reinforced Concrete Beams, One-way and Two-way Slab Systems ============================================================================= Copyright , Portland Cement Association All rights reserved Licensee stated above acknowledges that Portland Cement Association (PCA) is not and cannot be responsible for either the accuracy or adequacy of the material supplied as input for processing by the pcaslab computer program. Furthermore, PCA neither makes any warranty expressed nor implied with respect to the correctness of the output prepared by the pcaslab program. Although PCA has endeavored to produce pcaslab error free the program is not and cannot be certified infallible. The final and only responsibility for analysis, design and engineering documents is the licensees. Accordingly, PCA disclaims all responsibility in contract, negligence or other tort for any analysis, design or engineering documents prepared in connection with the use of the pcaslab program. ============================================================================================= [1] INPUT ECHO ============================================================================================= General Information: ==================== File name: c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Project: Time Saving Design Aids Frame: Two-Way Slab Engineer: PCA Code: ACI Reinforcement Database: ASTM A615 Mode: Design Number of supports = 4 Floor System: Two-Way Live load pattern ratio = 75% Minimum free edge for punching shear = 10 times slab thickness Deflections are based on cracked section properties. In negative moment regions, Ig and Mcr DO NOT include flange/slab contribution (if available) Long-term deflections are calculated for load duration of 60 months. 0% of live load is sustained. Compression reinforcement calculations NOT selected. Material Properties: ==================== Slabs Beams Columns wc = lb/ft3 f'c = 4 4 ksi Ec = ksi fr = ksi fy = 60 ksi, Bars are not epoxy-coated fyv = 60 ksi Es = ksi Reinforcement Database: =============== Units: Db (in), Ab (in^2), Wb (lb/ft) Size Db Ab Wb Size Db Ab Wb

11 TIME SAVING DESIGN AID Page 11 of 14 pcaslab v2.00 Portland Cement Association , 11:27:26 AM Licensed to: pcastructurepoint, License ID: D2DE-2C8D0 c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Page 2 # # # # # # # # # # # Span Data: ========== Slabs: L1, wl, wr (ft); t, Hmin (in) Span Loc L1 t wl wr Hmin Int Int Int Support Data: ============= Columns: c1a, c2a, c1b, c2b (in); Ha, Hb (ft) Supp c1a c2a Ha c1b c2b Hb Red% Boundary Conditions: Kz (kip/in); Kry (kip-in/rad) Supp Spring Kz Spring Kry Far End A Far End B Fixed Fixed Fixed Fixed Fixed Fixed Fixed Fixed Load Data: ========== Load Cases and Combinations: Case SELF Dead Live Type DEAD DEAD LIVE U U U U U U U U U U U U Span Loads: Span Case Wa Area Loads - Wa (lb/ft2): 1 Dead 30 2 Dead 30 3 Dead 30 1 Live 50 2 Live 50 3 Live 50 Support Loads - Fz (kip), My (k-ft): Supp Case Fz My SELF SELF SELF SELF Live Live Live Live 0 0 Support Displacements - D (in), R (rad): Supp Case D R SELF SELF SELF SELF Live Live Live Live 0 0

12 TIME SAVING DESIGN AID Page 12 of 14 pcaslab v2.00 Portland Cement Association , 11:27:26 AM Licensed to: pcastructurepoint, License ID: D2DE-2C8D0 c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Page 3 Reinforcement Criteria: ======================= Top bars Bottom bars Stirrups Min Max Min Max Min Max Slabs and Ribs: Bar Size #4 #8 #4 #8 Bar spacing in Reinf ratio % Cover in Beams: Bar Size #5 #8 #5 #8 #3 #5 Bar spacing in Reinf ratio % Cover in Side cover in Layer dist in No. of legs 2 6 ============================================================================================= [2] DESIGN RESULTS* ============================================================================================= *Unless otherwise noted, all results are in the direction of analysis only. Another analysis in the perpendicular direction has to be carried out for two-way slab systems. Top Reinforcement: ================== Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in) Span Strip Zone Width Mmax Xmax AsMin AsMax SpReq AsReq Bars Column Left #4 Middle Right #4 Middle Left Middle Right #4 2 Column Left #4 Middle Right #4 Middle Left #4 Middle Right #4 3 Column Left #4 Middle Right #4 Middle Left #4 Middle Right Top Bar Details: ================ Units: Length (ft) Left Continuous Right Span Strip Bars Length Bars Length Bars Length Bars Length Bars Length Column 10-# # # Middle # Column 12-# # # # Middle 14-# # Column 12-# # # Middle 14-# Bottom Reinforcement: ===================== Units: Width (ft), Mmax (k-ft), Xmax (ft), As (in^2), Sp (in) Span Strip Width Mmax Xmax AsMin AsMax SpReq AsReq Bars Column #4 Middle #4 2 Column #4 Middle #4 3 Column #4 Middle #4 Bottom Bar Details: ===================

13 TIME SAVING DESIGN AID Page 13 of 14 pcaslab v2.00 Portland Cement Association , 11:27:27 AM Licensed to: pcastructurepoint, License ID: D2DE-2C8D0 c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Page 4 Units: Start (ft), Length (ft) Long Bars Short Bars Span Strip Bars Start Length Bars Start Length Column 16-# Middle 14-# Column 10-# Middle 14-# Column 16-# Middle 14-# Flexural Capacity: ================== Units: x (ft), As (in^2), PhiMn (k-ft) Span Strip x AsTop AsBot PhiMn- PhiMn Column Middle Column Middle Column Middle

14 TIME SAVING DESIGN AID Page 14 of 14 pcaslab v2.00 Portland Cement Association , 11:27:27 AM Licensed to: pcastructurepoint, License ID: D2DE-2C8D0 c:\work\time Saving Design Aids\318-05\Rev 2\Data\.slb Page Slab Shear Capacity: ==================== Units: b, d (in), Xu (ft), PhiVc, Vu(kip) Span b d Vratio PhiVc Vu Xu Flexural Transfer of Negative Unbalanced Moment at Supports: ============================================================ Units: Width (in), Munb (k-ft), As (in^2) Supp Width GammaF*Munb Comb Pat AsReq AsProv Additional Bars U2 All # U2 Odd U2 Odd U2 All #4 Punching Shear Around Columns: ============================== Units: Vu (kip), Munb (k-ft), vu (psi), Phi*vc (psi) Supp Vu vu Munb Comb Pat GammaV vu Phi*vc U2 All U2 All U2 All U2 All Deflections: ============ Section properties Units: Ig, Icr, Ie (in^4), Mcr, Mmax (k-ft) Load Level Ie,avg Dead Dead+Live Span Dead Dead+Live Zone Ig Icr Mcr Mmax Ie Mmax Ie Middle Right Left Middle Right Left Middle Maximum Instantaneous Deflections - Direction of Analysis Units: D (in), Ig (in^4) Frame Strips Span Ddead Dlive Dtotal Strip Ig LDF Ratio Ddead Dlive Dtotal Column Middle Column Middle Column Middle Maximum Long-term Deflections - Direction of Analysis Time dependant factor for sustained loads = Units: D (in) Column Strip Middle Strip Span Dsust Lambda Dcs Dcs+lu Dcs+l Dtotal Dsust Lambda Dcs Dcs+lu Dcs+l Dtotal Material Takeoff: ================= Reinforcement in the Direction of Analysis Top Bars: lb <=> lb/ft <=> lb/ft^2 Bottom Bars: lb <=> lb/ft <=> lb/ft^2 Stirrups: 0.0 lb <=> 0.00 lb/ft <=> lb/ft^2 Total Steel: lb <=> lb/ft <=> lb/ft^2 Concrete: ft^3 <=> ft^3/ft <=> ft^3/ft^2