Project Name: General Description:Location:Client:Designer:Date:

DESIGN OF TWO-WAY SLAB

Design Specifications: T.B. - Transverse BarCoefficient Method: L.B. - Longitudinal BarYield Stresses: Top Bar

fy 276 Mpa Bottom Barfc' 20.7 Mpa Continues Edge /////////

Loading:Service Live Load 2.8 Kpa Top BarService Dead Load 2 Kpa Excluding slab weight)

11.00

Slab: M Ratio 0.70 Two - way SlabL - Long span 6 m.S - Short span 4 m. Min. hSlab h 120 mm => 111Concrete cover 25 mm

Case Number (#) 8 One long edge discontinues

Slab Reinforcement: diam. Ǿ 10 mmBar Area 78.54 mm²

Check for Shear: Check for Effective Depth:

Short Direction: SAFE!!!!! OKLong Direction: SAFE!!!!! OKReinforcement Ratio:

1.4/fy < ρ > .75ρb0.0051 0.01 0.0278

Case # Description Philippine Standard reinforcing Bars1 All Four Edges discontinues R - Bar Area Diameter2 All Four Edges continues 6 mm 28.27 63 Two long edges discontinues 10 mm 78.54 104 One long one short discontinues 12 mm 113.09 125 Two short edges discontinues 15 mm 176.71 156 Two short one long edge discontinues 20 mm 314.15 207 Two long one short edges discontinues 25 mm 490.86 258 One long edge discontinues 28 mm 615.73 289 One short edge discontinues 32 mm 804.22 32

Table. 1. COEFFICIENTS OF NEGATIVE MOMENTS IN SLABS

Longitudinal Bar

Ma, neg. = Ca, neg WLa² Where: W = Total dead + Live LoadMb, neg. = Cb,neg.WLb²M = 0.70 Case # 8

Coef.Case #

1 2 3 4 5 6 7

1Ca, neg. 0 0.045 0 0.05 0.075 0.071 0Cb, neg. 0 0.045 0.076 0.05 0 0 0.071

0.95Ca, neg. 0 0.05 0 0.055 0.079 0.075 0Cb, neg. 0 0.041 0.072 0.045 0 0 0.065

0.9Ca, neg. 0 0.055 0 0.06 0.08 0.079 0Cb, neg. 0 0.037 0.07 0.04 0 0 0.062

0.85Ca, neg. 0 0.06 0 0.066 0.082 0.083 0Cb, neg. 0 0.031 0.065 0.034 0 0 0.057

0.8Ca, neg. 0 0.065 0 0.071 0.083 0.086 0Cb, neg. 0 0.027 0.061 0.029 0 0 0.051

0.75Ca, neg. 0 0.069 0 0.076 0.085 0.088 0Cb, neg. 0 0.022 0.056 0.024 0 0 0.044

0.7Ca, neg. 0 0.074 0 0.081 0.086 0.091 0Cb, neg. 0 0.017 0.05 0.019 0 0 0.038

0.65Ca, neg. 0 0.077 0 0.085 0.087 0.093 0Cb, neg. 0 0.014 0.043 0.015 0 0 0.031

0.6Ca, neg. 0 0.081 0 0.089 0.088 0.095 0Cb, neg. 0 0.01 0.035 0.011 0 0 0.024

0.55Ca, neg. 0 0.084 0 0.092 0.089 0.096 0Cb, neg. 0 0.007 0.028 0.008 0 0 0.019

0.5Ca, neg. 0 0.068 0.094 0.09 0.097 0Cb, neg. 0 0.006 0.022 0.006 0 0 0.014

Table. 2. COEFFICIENTS FOR DEAD - LOAD POSITIVE MOMENTS IN SLABS

Ma, pos dL = Ca, dL WLa² Where: W = Total uniform deadloadMb, pos,Dl. = Cb,dLWLb²M = 0.70 Case # 8

Coef.Case #

1 2 3 4 5 6 7

1Ca, dL. 0.036 0.018 0.018 0.027 0.027 0.033 0.027Cb, dL 0.036 0.018 0.027 0.027 0.018 0.027 0.033

0.95Ca, dL. 0.04 0.02 0.021 0.03 0.028 0.036 0.031Cb, dL 0.033 0.016 0.025 0.024 0.015 0.024 0.031

0.9Ca, dL. 0.045 0.022 0.025 0.033 0.029 0.039 0.035Cb, dL 0.029 0.014 0.024 0.022 0.013 0.021 0.028

0.85Ca, dL. 0.05 0.024 0.029 0.036 0.031 0.042 0.04Cb, dL 0.026 0.012 0.022 0.019 0.011 0.017 0.025

0.8Ca, dL. 0.056 0.026 0.034 0.039 0.032 0.045 0.045Cb, dL 0.023 0.011 0.02 0.016 0.009 0.015 0.022

0.75Ca, dL. 0.061 0.028 0.04 0.043 0.033 0.048 0.051Cb, dL 0.019 0.009 0.018 0.013 0.007 0.012 0.02

0.7Ca, dL. 0.068 0.03 0.046 0.046 0.035 0.051 0.058Cb, dL 0.016 0.007 0.016 0.011 0.005 0.009 0.017

0.65Ca, dL. 0.074 0.032 0.054 0.05 0.036 0.054 0.065Cb, dL 0.013 0.006 0.014 0.009 0.004 0.007 0.014

0.6Ca, dL. 0.081 0.034 0.062 0.053 0.037 0.056 0.073Cb, dL 0.01 0.004 0.011 0.007 0.003 0.006 0.012

0.55Ca, dL. 0.088 0.035 0.071 0.056 0.038 0.058 0.081Cb, dL 0.008 0.003 0.009 0.005 0.002 0.004 0.009

Ratio: M=La/Lb

Ratio: M=La/Lb

0.5Ca, dL. 0.095 0.037 0.08 0.059 0.039 0.061 0.089Cb, dL 0.006 0.003 0.007 0.004 0.001 0.003 0.007

Table. 3. COEFFICIENTS FOR LIVE - LOAD POSITIVE MOMENTS IN SLABS

Ma, pos, LL = Ca, LL WLa² Where: W = Total uniform LiveloadMb, pos,LL. = Cb,LLWLb²M = 0.70 Case # 8

Coef.Case #

1 2 3 4 5 6 7

1Ca, dL. 0.036 0.027 0.027 0.032 0.032 0.035 0.032Cb, dL 0.036 0.027 0.032 0.032 0.027 0.032 0.035

0.95Ca, dL. 0.04 0.03 0.031 0.035 0.034 0.038 0.036Cb, dL 0.033 0.025 0.029 0.029 0.024 0.029 0.032

0.9Ca, dL. 0.045 0.034 0.035 0.039 0.037 0.042 0.04Cb, dL 0.029 0.022 0.027 0.026 0.021 0.025 0.029

0.85Ca, dL. 0.05 0.037 0.04 0.043 0.041 0.46 0.045Cb, dL 0.026 0.019 0.024 0.024 0.019 0.022 0.026

0.8Ca, dL. 0.056 0.041 0.045 0.048 0.044 0.051 0.051Cb, dL 0.023 0.017 0.022 0.02 0.016 0.019 0.023

0.75Ca, dL. 0.061 0.045 0.051 0.052 0.047 0.055 0.056Cb, dL 0.019 0.014 0.019 0.016 0.013 0.016 0.02

0.7Ca, dL. 0.068 0.049 0.057 0.057 0.051 0.06 0.063Cb, dL 0.016 0.012 0.016 0.014 0.011 0.013 0.017

0.65Ca, dL. 0.074 0.053 0.064 0.062 0.055 0.064 0.07Cb, dL 0.013 0.01 0.014 0.011 0.009 0.01 0.014

0.6Ca, dL. 0.081 0.058 0.071 0.067 0.059 0.068 0.077Cb, dL 0.01 0.007 0.011 0.009 0.007 0.008 0.011

0.55Ca, dL. 0.088 0.062 0.08 0.072 0.036 0.073 0.085Cb, dL 0.008 0.006 0.009 0.007 0.005 0.006 0.009

0.5Ca, dL. 0.095 0.066 0.088 0.077 0.067 0.078 0.092Cb, dL 0.006 0.004 0.007 0.005 0.004 0.005 0.007

Table. 4. RATIO OF LOAD w in La and Lb DIRECTIONS FOR SHEAR IN SLAB AND LOAD IN SUPPORTS

M = 0.70 Case # 8

Coef.Case #

1 2 3 4 5 6 7

1Wa 0.5 0.5 0.17 0.5 0.83 0.71 0.29Wb 0.5 0.5 0.83 0.5 0.17 0.29 0.71

0.95Wa 0.55 0.55 0.2 0.55 0.86 0.75 0.33Wb 0.45 0.45 0.8 0.45 0.14 0.25 0.67

0.9Wa 0.6 0.6 0.23 0.6 0.88 0.79 0.38Wb 0.4 0.4 0.77 0.4 0.12 0.21 0.62

0.85Wa 0.66 0.66 0.28 0.66 0.9 0.83 0.43Wb 0.34 0.34 0.72 0.34 0.1 0.17 0.57

0.8Wa 0.71 0.71 0.33 0.71 0.92 0.86 0.49Wb 0.29 0.29 0.67 0.29 0.08 0.14 0.51

0.75Wa 0.76 0.76 0.39 0.76 0.94 0.88 0.56Wb 0.24 0.24 0.61 0.24 0.06 0.12 0.44

0.7Wa 0.81 0.81 0.45 0.81 0.95 0.91 0.62Wb 0.19 0.19 0.55 0.19 0.05 0.09 0.38

0.65Wa 0.85 0.85 0.53 0.85 0.96 0.93 0.69Wb 0.15 0.15 0.47 0.15 0.04 0.07 0.31

Ratio: M=La/Lb

Ratio: M=La/Lb

0.6Wa 0.89 0.89 0.61 0.89 0.97 0.95 0.76Wb 0.11 0.11 0.39 0.11 0.03 0.05 0.24

0.55Wa 0.92 0.92 0.69 0.92 0.98 0.96 0.81Wb 0.08 0.08 0.31 0.08 0.02 0.04 0.19

0.5Wa 0.94 0.94 0.76 0.94 0.99 0.97 0.86Wb 0.06 0.06 0.24 0.06 0.01 0.03 0.14

Solution:

Slab Weight: 2,825.28 N/mm² 2.83 Kpa

Deadload: 4.83 KpaLiveload 2.80 Kpa

Wu = 1.4Wd + 1.7WLTotal Load, Wu = 11.52 Kpa

M = La/Lb 0.70

Considering 1 meter strip: 11.52 Kn/m

AT SHORT DIRECTION:

Negative Moment at Continues Edges (Top Bars)Ca, neg. 0.068Ma, neg. = Ca, neg WLa² 12.53 Kn-mPositive Moment at Midspan (Bottom Bars)Deadload, Ca 0.04Ma, pos, dL = CaWLa² 4.32 Kn-mLiveload, Ca 0.054Ma, pos, LL = CaWLa² 4.11 Kn-m

Ma, pos.(dL+LL) 8.44 Kn-mNegative Moment at Discontinues Edge (1/3 pos. moment) Top BarsMa, neg. = Ma,pos(dL+LL)/3 2.81 Kn-m

AT LONG DIRECTION:

Negative Moment at Continues Edges (Top Bars)Cb, neg. 0.029Mb, neg. = Cb, neg WLb² 12.02 Kn-mPositive Moment at Midspan (Bottom Bars)Deadload, Cb 0.011Ma, pos, dL = CbWLb² 2.68 Kn-mLiveload, Cb 0.054Ma, pos, LL = CbWLb² 9.25 Kn-m

Ma, pos.(dL+LL) 11.93 Kn-mNegative Moment at Discontinues Edge (1/3 pos. moment) Top BarsMa, neg. = Ma,pos(dL+LL)/3 3.98 Kn-m

SHORT SPAN LONG SPANCont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.Edge

ρmin. = 1.4/fy 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051ρmax = .75(β)²(fc'/fy)(600/(600+fy)) 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278ρ (Selected) 0.01 0.01 0.01 0.01 0.01 0.01m = fy/.85fc' 15.686 15.686 15.686 15.686 15.686 15.686Rn = ρfy(1-ρm/2) 2.544 2.544 2.544 2.544 2.544 2.544

Max. Ultimate Moment Mu = 12.53 8.44 2.81 12.02 9.25 3.98 Mn = Mu/.9 13.92 9.37 3.12 13.36 10.28 4.42 Req. d = sqrt(Mn/bRn), mm 73.98 60.71 35.05 72.47 63.58 41.68Req. h = d+1/2bar dia.+bar dia.+cover 113.98 100.71 75.05 112.47 103.58 81.68 Min. h = 2(L+S)*1000/180 111.11 111.11 111.11 111.11 111.11 111.11

Actual h = 120 120 120 120 120 120Effective d = h - (bar dia. + 1/2 bar dia) 96.11 101.11 101.11 96.11

OK OK OK OK

SHORT SPAN LONG SPANTop Bar Bottom Bar Bottom Bar Top Bar Bottom Bar Bottom Bar

Cont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.EdgeMax. Ultimate Moment, Mu = 12.53 8.44 2.81 12.02 9.25 3.98 Mn = Mu/.90 13.92 9.37 3.12 13.36 10.28 4.42 Rn = Mn/bd² 2.544 2.544 2.544 2.544 2.544 2.544 ρmin. = 1.4/fy 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051ρmax = .75(β)²(fc'/fy)(600/(600+fy)) 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278ρ = 1/m(1 - sqrt(1-2mRn/fy) 0.01 0.01 0.01 0.01 0.0100 0.01As = ρbd 739.800 607.059 350.486 724.686 635.787 416.768Reinf. Bar diameter, mm 10 10 10 10 10 10Reinf. Bar Spacing, mm 106.16 129.38 224.09 108.38 123.53 188.45 Min. Spacing, 3h 341.94 302.12 225.15 337.41 310.74 245.03 Final Bar Spacing, cm. 11.00 13.00 22.00 11.00 12.00 19.00

Check for Shear:

Load on Supporting Beams:

W = wuLS 276.37 Kn

Short Direction:Wa = Shear ratio on slab 0.68Ws = Wa*wu 187.93 Kn

23.49 Kn

ØVc = .85(.17)(√fc')(Eff. d) 66.47 Kn SAFE!!!!!

Long Direction:Wb = Shear ratio on slab 0.32WL = Wb*wu 88.44 Kn

7.37 Kn

ØVc = .85(.17)(√fc')(Eff. d) 63.19 Kn SAFE!!!!!

Load per meter on short beam, Ws/2S

Load per meter on short beam, Wb/2L

Transverse Bars10 mm. @ 10 mm. @

Top Bar 11.00 cm. oc 11.00 cm. oc10 mm. @

Bot.Bar cm. oc 12.00 cm. oc cm. oc

////////////// ////////////// ////////////// ////////////// ////////////// //////////////Bot.Bar '///// /////

10 mm. @ '///// ///// 1 m. cm.oc '///// /////

'///// ///// '///// ///// '///// /////

10 mm. @ '///// ///// 2 m. 13.00 cm. oc '///// /////

'///// ///// '///// ///// '///// /////

10 mm. @ '///// ///// 1 m. 22.00 cm. oc '///// /////

'///// /////. . . . . . . . . . . .

1.5 m. 3 m. 1.5 m.

Case # L Top L Bottom S Left S Right1 . . . . . . . . All Four Edges discontinues2 ////////////// ////////////// '///// ///// All Four Edges continues3 . . . . '///// ///// Two long edges discontinues4 . . ////////////// '///// . . One long one short discontinues5 ////////////// ////////////// . . . . Two short edges discontinues6 ////////////// . . . . . . Two short one long edge discontinues7 . . . . . . ///// Two long one short edges discontinues8 ////////////// . . '///// ///// One long edge discontinues9 ////////////// ////////////// '///// . . One short edge discontinues

////////////// . . '///// /////

Case #8 9

0.033 0.061 0.033 0.0680.061 0.033 0.061 0.0290.038 0.065 0.0380.056 0.029 0.0560.043 0.068 0.0430.052 0.025 0.0520.049 0.072 0.0490.046 0.021 0.0460.055 0.075 0.0550.041 0.017 0.0410.061 0.078 0.0610.036 0.014 0.0360.068 0.081 0.0680.029 0.011 0.0290.074 0.083 0.0740.024 0.008 0.024

0.08 0.085 0.080.018 0.006 0.0180.085 0.086 0.0850.014 0.005 0.0140.089 0.088 0.089

0.01 0.003 0.01

Case #8 90.02 0.023 0.02 0.04

0.023 0.023 0.023 0.0110.022 0.024 0.0220.021 0.017 0.0210.025 0.026 0.0250.019 0.015 0.0190.029 0.028 0.0290.017 0.013 0.0170.032 0.029 0.0320.015 0.01 0.0150.036 0.031 0.0360.013 0.007 0.013

0.04 0.033 0.040.011 0.006 0.0110.044 0.034 0.0440.009 0.005 0.0090.048 0.036 0.0480.007 0.004 0.0070.052 0.037 0.0520.005 0.003 0.005

0.056 0.038 0.0560.004 0.002 0.004

Case #8 9

0.028 0.03 0.028 0.0540.03 0.028 0.03 0.014

0.031 0.032 0.0310.027 0.025 0.0270.035 0.036 0.0350.024 0.022 0.024

0.04 0.039 0.040.022 0.02 0.0220.044 0.042 0.0440.019 0.017 0.0190.049 0.046 0.0490.016 0.013 0.0160.054 0.05 0.0540.014 0.011 0.0140.059 0.054 0.0590.011 0.009 0.0110.065 0.059 0.0650.009 0.007 0.009

0.07 0.063 0.070.007 0.006 0.0070.076 0.067 0.0760.005 0.004 0.005

Case #8 90.33 0.67 0.33 0.680.67 0.33 0.67 0.320.38 0.71 0.380.62 0.29 0.620.43 0.75 0.430.57 0.25 0.570.49 0.79 0.490.51 0.21 0.510.55 0.83 0.550.45 0.17 0.450.61 0.86 0.610.39 0.14 0.390.68 0.898 0.680.32 0.11 0.320.74 0.92 0.740.26 0.08 0.26

0.8 0.94 0.80.2 0.06 0.2

0.85 0.85 0.850.15 0.15 0.150.89 0.97 0.890.11 0.03 0.11