Project Name: General Description:

Location:
Client:
Designer:
Date:

DESIGN OF TWO-WAY SLAB

Design Specifications: T.B. - Transverse Bar

Coefficient Method: L.B. - Longitudinal Bar
Yield Stresses: Top Bar
fy 276 Mpa Bottom Bar
fc' 20.7 Mpa Continues Edge /////////

Loading:
Service Live Load 2.8 Kpa L Top Bar
Service Dead Load 2 Kpa Excluding slab weight) o
n 11.00
g
Slab: M Ratio 0.70 Two - way Slab
i
L - Long span 6 m. t
S - Short span 4 m. Min. h u
Slab h 120 mm => 111 d
Concrete cover 25 mm i
n
Case Number (#) 8 One long edge discontinues a
l
Slab Reinforcement: diam. Ǿ 10 mm B
Bar Area 78.54 mm² a
r
Check for Shear: Check for Effective Depth:
Short Direction: SAFE!!!!! OK
Long Direction: SAFE!!!!! OK
Reinforcement Ratio:
1.4/fy <ρ> .75ρb
0.0051 0.01 0.0278

Case # Description Philippine Standard reinforcing Bars

1 All Four Edges discontinues R - Bar Area Diameter
2 All Four Edges continues 6 mm 28.27 6
3 Two long edges discontinues 10 mm 78.54 10
4 One long one short discontinues 12 mm 113.09 12
5 Two short edges discontinues 15 mm 176.71 15
6 Two short one long edge discontinues 20 mm 314.15 20
7 Two long one short edges discontinues 25 mm 490.86 25
8 One long edge discontinues 28 mm 615.73 28
9 One short edge discontinues 32 mm 804.22 32

Table. 1. COEFFICIENTS OF NEGATIVE MOMENTS IN SLABS

Ma, neg. = Ca, neg WLa² Where: W = Total dead + Live Load
Mb, neg. = Cb,neg.WLb²
M= 0.70 Case # 8
Ratio: Case #
Coef.
M=La/Lb 1 2 3 4 5 6 7
Ca, neg. 0 0.045 0 0.05 0.075 0.071 0
1
Cb, neg. 0 0.045 0.076 0.05 0 0 0.071
Ca, neg. 0 0.05 0 0.055 0.079 0.075 0
0.95
Cb, neg. 0 0.041 0.072 0.045 0 0 0.065
Ca, neg. 0 0.055 0 0.06 0.08 0.079 0
0.9
Cb, neg. 0 0.037 0.07 0.04 0 0 0.062
Ca, neg. 0 0.06 0 0.066 0.082 0.083 0
0.85
Cb, neg. 0 0.031 0.065 0.034 0 0 0.057
Ca, neg. 0 0.065 0 0.071 0.083 0.086 0
0.8
Cb, neg. 0 0.027 0.061 0.029 0 0 0.051
Ca, neg. 0 0.069 0 0.076 0.085 0.088 0
0.75
Cb, neg. 0 0.022 0.056 0.024 0 0 0.044
Ca, neg. 0 0.074 0 0.081 0.086 0.091 0
0.7
Cb, neg. 0 0.017 0.05 0.019 0 0 0.038
Ca, neg. 0 0.077 0 0.085 0.087 0.093 0
0.65
Cb, neg. 0 0.014 0.043 0.015 0 0 0.031
Ca, neg. 0 0.081 0 0.089 0.088 0.095 0
0.6
Cb, neg. 0 0.01 0.035 0.011 0 0 0.024
Ca, neg. 0 0.084 0 0.092 0.089 0.096 0
0.55
Cb, neg. 0 0.007 0.028 0.008 0 0 0.019
Ca, neg. 0 0.068 0.094 0.09 0.097 0
0.5
Cb, 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 deadload

Mb, pos,Dl. = Cb,dLWLb²
M= 0.70 Case # 8
Ratio: Case #
Coef.
M=La/Lb 1 2 3 4 5 6 7
Ca, dL. 0.036 0.018 0.018 0.027 0.027 0.033 0.027
1
Cb, dL 0.036 0.018 0.027 0.027 0.018 0.027 0.033
Ca, dL. 0.04 0.02 0.021 0.03 0.028 0.036 0.031
0.95
Cb, dL 0.033 0.016 0.025 0.024 0.015 0.024 0.031
Ca, dL. 0.045 0.022 0.025 0.033 0.029 0.039 0.035
0.9
Cb, dL 0.029 0.014 0.024 0.022 0.013 0.021 0.028
Ca, dL. 0.05 0.024 0.029 0.036 0.031 0.042 0.04
0.85
Cb, dL 0.026 0.012 0.022 0.019 0.011 0.017 0.025
Ca, dL. 0.056 0.026 0.034 0.039 0.032 0.045 0.045
0.8
Cb, dL 0.023 0.011 0.02 0.016 0.009 0.015 0.022
Ca, dL. 0.061 0.028 0.04 0.043 0.033 0.048 0.051
0.75
Cb, dL 0.019 0.009 0.018 0.013 0.007 0.012 0.02
Ca, dL. 0.068 0.03 0.046 0.046 0.035 0.051 0.058
0.7
Cb, dL 0.016 0.007 0.016 0.011 0.005 0.009 0.017
Ca, dL. 0.074 0.032 0.054 0.05 0.036 0.054 0.065
0.65
Cb, dL 0.013 0.006 0.014 0.009 0.004 0.007 0.014
Ca, dL. 0.081 0.034 0.062 0.053 0.037 0.056 0.073
0.6
Cb, dL 0.01 0.004 0.011 0.007 0.003 0.006 0.012
Ca, dL. 0.088 0.035 0.071 0.056 0.038 0.058 0.081
0.55
Cb, dL 0.008 0.003 0.009 0.005 0.002 0.004 0.009
 Ca, dL. 0.095 0.037 0.08 0.059 0.039 0.061 0.089
0.5
Cb, 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 Liveload

Mb, pos,LL. = Cb,LLWLb²
M= 0.70 Case # 8
Ratio: Case #
Coef.
M=La/Lb 1 2 3 4 5 6 7
Ca, dL. 0.036 0.027 0.027 0.032 0.032 0.035 0.032
1
Cb, dL 0.036 0.027 0.032 0.032 0.027 0.032 0.035
Ca, dL. 0.04 0.03 0.031 0.035 0.034 0.038 0.036
0.95
Cb, dL 0.033 0.025 0.029 0.029 0.024 0.029 0.032
Ca, dL. 0.045 0.034 0.035 0.039 0.037 0.042 0.04
0.9
Cb, dL 0.029 0.022 0.027 0.026 0.021 0.025 0.029
Ca, dL. 0.05 0.037 0.04 0.043 0.041 0.46 0.045
0.85
Cb, dL 0.026 0.019 0.024 0.024 0.019 0.022 0.026
Ca, dL. 0.056 0.041 0.045 0.048 0.044 0.051 0.051
0.8
Cb, dL 0.023 0.017 0.022 0.02 0.016 0.019 0.023
Ca, dL. 0.061 0.045 0.051 0.052 0.047 0.055 0.056
0.75
Cb, dL 0.019 0.014 0.019 0.016 0.013 0.016 0.02
Ca, dL. 0.068 0.049 0.057 0.057 0.051 0.06 0.063
0.7
Cb, dL 0.016 0.012 0.016 0.014 0.011 0.013 0.017
Ca, dL. 0.074 0.053 0.064 0.062 0.055 0.064 0.07
0.65
Cb, dL 0.013 0.01 0.014 0.011 0.009 0.01 0.014
Ca, dL. 0.081 0.058 0.071 0.067 0.059 0.068 0.077
0.6
Cb, dL 0.01 0.007 0.011 0.009 0.007 0.008 0.011
Ca, dL. 0.088 0.062 0.08 0.072 0.036 0.073 0.085
0.55
Cb, dL 0.008 0.006 0.009 0.007 0.005 0.006 0.009
Ca, dL. 0.095 0.066 0.088 0.077 0.067 0.078 0.092
0.5
Cb, 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
Ratio: Case #
Coef.
M=La/Lb 1 2 3 4 5 6 7
Wa 0.5 0.5 0.17 0.5 0.83 0.71 0.29
1
Wb 0.5 0.5 0.83 0.5 0.17 0.29 0.71
Wa 0.55 0.55 0.2 0.55 0.86 0.75 0.33
0.95
Wb 0.45 0.45 0.8 0.45 0.14 0.25 0.67
Wa 0.6 0.6 0.23 0.6 0.88 0.79 0.38
0.9
Wb 0.4 0.4 0.77 0.4 0.12 0.21 0.62
Wa 0.66 0.66 0.28 0.66 0.9 0.83 0.43
0.85
Wb 0.34 0.34 0.72 0.34 0.1 0.17 0.57
Wa 0.71 0.71 0.33 0.71 0.92 0.86 0.49
0.8
Wb 0.29 0.29 0.67 0.29 0.08 0.14 0.51
Wa 0.76 0.76 0.39 0.76 0.94 0.88 0.56
0.75
Wb 0.24 0.24 0.61 0.24 0.06 0.12 0.44
Wa 0.81 0.81 0.45 0.81 0.95 0.91 0.62
0.7
Wb 0.19 0.19 0.55 0.19 0.05 0.09 0.38
Wa 0.85 0.85 0.53 0.85 0.96 0.93 0.69
0.65
Wb 0.15 0.15 0.47 0.15 0.04 0.07 0.31
 Wa 0.89 0.89 0.61 0.89 0.97 0.95 0.76
0.6
Wb 0.11 0.11 0.39 0.11 0.03 0.05 0.24
Wa 0.92 0.92 0.69 0.92 0.98 0.96 0.81
0.55
Wb 0.08 0.08 0.31 0.08 0.02 0.04 0.19
Wa 0.94 0.94 0.76 0.94 0.99 0.97 0.86
0.5
Wb 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 Kpa
Liveload 2.80 Kpa
Wu = 1.4Wd + 1.7WL
Total 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. 0.068
Ma, neg. = Ca, neg WLa² 12.53 Kn-m
Positive Moment at Midspan (Bottom Bars)
Deadload, Ca 0.04
Ma, pos, dL = CaWLa² 4.32 Kn-m
Liveload, Ca 0.054
Ma, pos, LL = CaWLa² 4.11 Kn-m
Ma, pos.(dL+LL) 8.44 Kn-m
Negative Moment at Discontinues Edge (1/3 pos. moment) Top Bars
Ma, neg. = Ma,pos(dL+LL)/3 2.81 Kn-m

AT LONG DIRECTION:

Negative Moment at Continues Edges (Top Bars)

Cb, neg. 0.029
Mb, neg. = Cb, neg WLb² 12.02 Kn-m
Positive Moment at Midspan (Bottom Bars)
Deadload, Cb 0.011
Ma, pos, dL = CbWLb² 2.68 Kn-m
Liveload, Cb 0.054
Ma, pos, LL = CbWLb² 9.25 Kn-m
Ma, pos.(dL+LL) 11.93 Kn-m
Negative Moment at Discontinues Edge (1/3 pos. moment) Top Bars
Ma, neg. = Ma,pos(dL+LL)/3 3.98 Kn-m

SHORT SPAN LONG SPAN

Cont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.Edge
ρmin. = 1.4/fy 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051
ρmax = .75(β)²(fc'/fy)(600/(600+fy)) 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278
ρ (Selected) 0.01 0.01 0.01 0.01 0.01 0.01
m = fy/.85fc' 15.686 15.686 15.686 15.686 15.686 15.686
Rn = 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 41.68
Req. 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 = 120 120 120 120 120 120
Effective d = h - (bar dia. + 1/2 bar dia) 96.11 101.11 101.11 96.11
OK OK OK OK

SHORT SPAN LONG SPAN

Top Bar Bottom Bar Bottom Bar Top Bar Bottom Bar Bottom Bar
Cont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.Edge
Max. 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 0.0051
ρmax = .75(β)²(fc'/fy)(600/(600+fy)) 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278
ρ = 1/m(1 - sqrt(1-2mRn/fy) 0.01 0.01 0.01 0.01 0.0100 0.01
As = ρbd 739.800 607.059 350.486 724.686 635.787 416.768
Reinf. Bar diameter, mm 10 10 10 10 10 10
Reinf. 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 0.68
Ws = Wa*wu 187.93 Kn
Load per meter on short beam,
23.49 Kn
Ws/2S
ØVc = .85(.17)(√fc')(Eff. d) 66.47 Kn SAFE!!!!!

Long Direction:
Wb = Shear ratio on slab 0.32
WL = Wb*wu 88.44 Kn
Load per meter on short beam,
7.37 Kn
Wb/2L
ØVc = .85(.17)(√fc')(Eff. d) 63.19 Kn SAFE!!!!!
 Transverse Bars
10 mm. @ 10 mm. @
Top Bar 11.00 cm. oc 11.00 cm. oc
10 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 Right

1 . . . . . . . . All Four Edges discontinues
2 ////////////// ////////////// '///// ///// All Four Edges continues
3 . . . . '///// ///// Two long edges discontinues
4 . . ////////////// '///// . . One long one short discontinues
5 ////////////// ////////////// . . . . Two short edges discontinues
6 ////////////// . . . . . . Two short one long edge discontinues
7 . . . . . . ///// Two long one short edges discontinues
8 ////////////// . . '///// ///// One long edge discontinues
9 ////////////// ////////////// '///// . . One short edge discontinues
////////////// . . '///// /////
 8 9
0.033 0.061 0.033 0.068
0.061 0.033 0.061 0.029
0.038 0.065 0.038
0.056 0.029 0.056
0.043 0.068 0.043
0.052 0.025 0.052
0.049 0.072 0.049
0.046 0.021 0.046
0.055 0.075 0.055
0.041 0.017 0.041
0.061 0.078 0.061
0.036 0.014 0.036
0.068 0.081 0.068
0.029 0.011 0.029
0.074 0.083 0.074
0.024 0.008 0.024
0.08 0.085 0.08
0.018 0.006 0.018
0.085 0.086 0.085
0.014 0.005 0.014
0.089 0.088 0.089
0.01 0.003 0.01

8 9
0.02 0.023 0.02 0.04
0.023 0.023 0.023 0.011
0.022 0.024 0.022
0.021 0.017 0.021
0.025 0.026 0.025
0.019 0.015 0.019
0.029 0.028 0.029
0.017 0.013 0.017
0.032 0.029 0.032
0.015 0.01 0.015
0.036 0.031 0.036
0.013 0.007 0.013
0.04 0.033 0.04
0.011 0.006 0.011
0.044 0.034 0.044
0.009 0.005 0.009
0.048 0.036 0.048
0.007 0.004 0.007
0.052 0.037 0.052
0.005 0.003 0.005
0.056 0.038 0.056
0.004 0.002 0.004

8 9
0.028 0.03 0.028 0.054
0.03 0.028 0.03 0.014
0.031 0.032 0.031
0.027 0.025 0.027
0.035 0.036 0.035
0.024 0.022 0.024
0.04 0.039 0.04
0.022 0.02 0.022
0.044 0.042 0.044
0.019 0.017 0.019
0.049 0.046 0.049
0.016 0.013 0.016
0.054 0.05 0.054
0.014 0.011 0.014
0.059 0.054 0.059
0.011 0.009 0.011
0.065 0.059 0.065
0.009 0.007 0.009
0.07 0.063 0.07
0.007 0.006 0.007
0.076 0.067 0.076
0.005 0.004 0.005

8 9
0.33 0.67 0.33 0.68
0.67 0.33 0.67 0.32
0.38 0.71 0.38
0.62 0.29 0.62
0.43 0.75 0.43
0.57 0.25 0.57
0.49 0.79 0.49
0.51 0.21 0.51
0.55 0.83 0.55
0.45 0.17 0.45
0.61 0.86 0.61
0.39 0.14 0.39
0.68 0.898 0.68
0.32 0.11 0.32
0.74 0.92 0.74
0.26 0.08 0.26
 0.8 0.94 0.8
0.2 0.06 0.2
0.85 0.85 0.85
0.15 0.15 0.15
0.89 0.97 0.89
0.11 0.03 0.11