Two Way Slab
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Project Name: Location: Client: Designer: Date:
General Description:
DESIGN OF TWO-WAY SLAB Design Specifications: Coefficient Method: Yield Stresses: fy fc'
276 20.7
Mpa Mpa
Loading: Service Live Load Service Dead Load
2.8 2
Kpa Kpa
Slab: M Ratio L - Long span S - Short span Slab h Concrete cover
0.70
6 4 120 25 8
Slab Reinforcement: diam. Ǿ Bar Area
10 78.54
Check for Shear:
Case # 1 2 3 4 5 6 7 8 9
Excluding slab weight)
Two - way Slab
Case Number (#)
Short Direction: Long Direction: Reinforcement Ratio: 1.4/fy <ρ> 0.0051 0.01
T.B. - Transverse Bar L.B. - Longitudinal Bar Top Bar Bottom Bar Continues Edge
m. m. mm mm
=>
Min. h 111
One long edge discontinues mm mm²
L o n g i t u d i n a l B a r
Check for Effective Depth:
SAFE!!!!! SAFE!!!!!
OK OK
.75ρb 0.0278
Description All Four Edges discontinues All Four Edges continues Two long edges discontinues One long one short discontinues Two short edges discontinues Two short one long edge discontinues Two long one short edges discontinues One long edge discontinues One short edge discontinues
Philippine Standard reinforcing Bars R - Bar Area Diameter 6 mm 28.27 6 10 mm 78.54 10 12 mm 113.09 12 15 mm 176.71 15 20 mm 314.15 20 25 mm 490.86 25 28 mm 615.73 28 32 mm 804.22 32
Table. 1. COEFFICIENTS OF NEGATIVE MOMENTS IN SLABS
/////////
Top Bar 11.00
Ma, neg. = Ca, neg WLa² Mb, neg. = Cb,neg.WLb² M= 0.70 Ratio: Coef. M=La/Lb Ca, neg. 1 Cb, neg. Ca, neg. 0.95 Cb, neg. Ca, neg. 0.9 Cb, neg. Ca, neg. 0.85 Cb, neg. Ca, neg. 0.8 Cb, neg. Ca, neg. 0.75 Cb, neg. Ca, neg. 0.7 Cb, neg. Ca, neg. 0.65 Cb, neg. Ca, neg. 0.6 Cb, neg. Ca, neg. 0.55 Cb, neg. Ca, neg. 0.5 Cb, neg.
Where: W = Total dead + Live Load Case #
8
1
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0.05 0.05 0.05 0.04 0.06 0.04 0.06 0.03 0.07 0.03 0.07 0.02 0.07 0.02 0.08 0.01 0.08 0.01 0.08 0.01 0.07 0.01
Case # 5
4 0 0.08 0 0.07 0 0.07 0 0.07 0 0.06 0 0.06 0 0.05 0 0.04 0 0.04 0 0.03
0.05 0.05 0.06 0.05 0.06 0.04 0.07 0.03 0.07 0.03 0.08 0.02 0.08 0.02 0.09 0.02 0.09 0.01 0.09 0.01 0.09 0.01
0.02
6 0.08 0 0.08 0 0.08 0 0.08 0 0.08 0 0.09 0 0.09 0 0.09 0 0.09 0 0.09 0 0.09 0
7 0.07 0 0.08 0 0.08 0 0.08 0 0.09 0 0.09 0 0.09 0 0.09 0 0.1 0 0.1 0 0.1 0
0 0.07 0 0.07 0 0.06 0 0.06 0 0.05 0 0.04 0 0.04 0 0.03 0 0.02 0 0.02 0 0.01
Table. 2. COEFFICIENTS FOR DEAD - LOAD POSITIVE MOMENTS IN SLABS Ma, pos dL = Ca, dL WLa² Mb, pos,Dl. = Cb,dLWLb² M= 0.70 Case # Ratio: Coef. M=La/Lb 1 Ca, dL. 0.04 1 Cb, dL 0.04 Ca, dL. 0.04 0.95 Cb, dL 0.03 Ca, dL. 0.05 0.9 Cb, dL 0.03 Ca, dL. 0.05 0.85 Cb, dL 0.03 Ca, dL. 0.06 0.8 Cb, dL 0.02 Ca, dL. 0.06 0.75 Cb, dL 0.02 Ca, dL. 0.07 0.7 Cb, dL 0.02 Ca, dL. 0.07 0.65 Cb, dL 0.01 Ca, dL. 0.08 0.6 Cb, dL 0.01 Ca, dL. 0.09 0.55 Cb, dL 0.01
Where: W = Total uniform deadload 8 2
3 0.02 0.02 0.02 0.02 0.02 0.01 0.02 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0 0.04 0
Case # 5
4 0.02 0.03 0.02 0.03 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01
0.03 0.03 0.03 0.02 0.03 0.02 0.04 0.02 0.04 0.02 0.04 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01
6 0.03 0.02 0.03 0.02 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.04 0.01 0.04 0 0.04 0 0.04 0
7 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0
0.03 0.03 0.03 0.03 0.04 0.03 0.04 0.03 0.05 0.02 0.05 0.02 0.06 0.02 0.07 0.01 0.07 0.01 0.08 0.01
0.5
Ca, dL. Cb, dL
0.1 0.01
0.04 0
0.08 0.01
0.06 0
0.04 0
0.06 0
0.09 0.01
Table. 3. COEFFICIENTS FOR LIVE - LOAD POSITIVE MOMENTS IN SLABS Ma, pos, LL = Ca, LL WLa² Mb, pos,LL. = Cb,LLWLb² M= 0.70 Case # Ratio: Coef. M=La/Lb 1 Ca, dL. 0.04 1 Cb, dL 0.04 Ca, dL. 0.04 0.95 Cb, dL 0.03 Ca, dL. 0.05 0.9 Cb, dL 0.03 Ca, dL. 0.05 0.85 Cb, dL 0.03 Ca, dL. 0.06 0.8 Cb, dL 0.02 Ca, dL. 0.06 0.75 Cb, dL 0.02 Ca, dL. 0.07 0.7 Cb, dL 0.02 Ca, dL. 0.07 0.65 Cb, dL 0.01 Ca, dL. 0.08 0.6 Cb, dL 0.01 Ca, dL. 0.09 0.55 Cb, dL 0.01 Ca, dL. 0.1 0.5 Cb, dL 0.01
Where: W = Total uniform Liveload 8 2
3 0.03 0.03 0.03 0.03 0.03 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.07 0
Case # 5
4 0.03 0.03 0.03 0.03 0.04 0.03 0.04 0.02 0.05 0.02 0.05 0.02 0.06 0.02 0.06 0.01 0.07 0.01 0.08 0.01 0.09 0.01
0.03 0.03 0.04 0.03 0.04 0.03 0.04 0.02 0.05 0.02 0.05 0.02 0.06 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
6 0.03 0.03 0.03 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.04 0.01 0.07 0
7 0.04 0.03 0.04 0.03 0.04 0.03 0.46 0.02 0.05 0.02 0.06 0.02 0.06 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
0.03 0.04 0.04 0.03 0.04 0.03 0.05 0.03 0.05 0.02 0.06 0.02 0.06 0.02 0.07 0.01 0.08 0.01 0.09 0.01 0.09 0.01
Table. 4. RATIO OF LOAD w in La and Lb DIRECTIONS FOR SHEAR IN SLAB AND LOAD IN SUPPORTS M= Ratio: M=La/Lb 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65
0.70 Coef. Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb
Case #
8
1
2 0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
3 0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
Case # 5
4 0.17 0.83 0.2 0.8 0.23 0.77 0.28 0.72 0.33 0.67 0.39 0.61 0.45 0.55 0.53 0.47
0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
6 0.83 0.17 0.86 0.14 0.88 0.12 0.9 0.1 0.92 0.08 0.94 0.06 0.95 0.05 0.96 0.04
7 0.71 0.29 0.75 0.25 0.79 0.21 0.83 0.17 0.86 0.14 0.88 0.12 0.91 0.09 0.93 0.07
0.29 0.71 0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.56 0.44 0.62 0.38 0.69 0.31
0.6 0.55 0.5
Wa Wb Wa Wb Wa Wb
0.89 0.11 0.92 0.08 0.94 0.06
0.89 0.11 0.92 0.08 0.94 0.06
0.61 0.39 0.69 0.31 0.76 0.24
0.89 0.11 0.92 0.08 0.94 0.06
0.97 0.03 0.98 0.02 0.99 0.01
0.95 0.05 0.96 0.04 0.97 0.03
0.76 0.24 0.81 0.19 0.86 0.14
Solution: Slab Weight:
2,825.28 2.83 4.83 2.80
Deadload: Liveload Wu = 1.4Wd + 1.7WL Total Load, Wu = M = La/Lb Considering 1 meter strip:
11.52
N/mm² Kpa Kpa Kpa Kpa
0.70 11.52 Kn/m
AT SHORT DIRECTION: Negative Moment at Continues Edges (Top Bars) Ca, neg. 0.07 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 0.05 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. 0.03 Mb, neg. = Cb, neg WLb² 12.02 Kn-m Positive Moment at Midspan (Bottom Bars) Deadload, Cb 0.01 Ma, pos, dL = CbWLb² 2.68 Kn-m Liveload, Cb 0.05 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
ρmin. = 1.4/fy ρmax = .75(β)²(fc'/fy)(600/(600+fy)) ρ (Selected) m = fy/.85fc' Rn = ρfy(1-ρm/2)
SHORT SPAN LONG SPAN Cont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.Edge 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.01 0.01 0.01 0.01 0.01 0.01 15.686 15.686 15.686 15.686 15.686 15.686 2.544 2.544 2.544 2.544 2.544 2.544
Max. Ultimate Moment Mu = Mn = Mu/.9 Req. d = sqrt(Mn/bRn), mm Req. h = d+1/2bar dia.+bar dia.+cover Min. h = 2(L+S)*1000/180 Actual h = Effective d = h - (bar dia. + 1/2 bar dia)
Max. Ultimate Moment, Mu = Mn = Mu/.90 Rn = Mn/bd² ρmin. = 1.4/fy ρmax = .75(β)²(fc'/fy)(600/(600+fy)) ρ = 1/m(1 - sqrt(1-2mRn/fy) As = ρbd Reinf. Bar diameter, mm Reinf. Bar Spacing, mm Min. Spacing, 3h Final Bar Spacing, cm.
12.53 13.92 73.98 113.98 111.11 120 96.11 OK
8.44 9.37 60.71 100.71 111.11 120 101.11 OK
2.81 3.12 35.05 75.05 111.11 120
Load on Supporting Beams: 276.37
Kn
0.68 187.93
Kn
Short Direction: Wa = Shear ratio on slab Ws = Wa*wu Load per meter on short beam, Ws/2S ØVc = .85(.17)(√fc')(Eff. d)
23.49
Kn
66.47
Kn
0.32 88.44
Kn
SAFE!!!!!
Long Direction: Wb = Shear ratio on slab WL = Wb*wu Load per meter on short beam, Wb/2L ØVc = .85(.17)(√fc')(Eff. d)
9.25 10.28 63.58 103.58 111.11 120 96.11 OK
3.98 4.42 41.68 81.68 111.11 120
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 12.53 8.44 2.81 12.02 9.25 3.98 13.92 9.37 3.12 13.36 10.28 4.42 2.544 2.544 2.544 2.544 2.544 2.544 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.01 0.01 0.01 0.01 0.0100 0.01 739.800 607.059 350.486 724.686 635.787 416.768 10 10 10 10 10 10 106.16 129.38 224.09 108.38 123.53 188.45 341.94 302.12 225.15 337.41 310.74 245.03 11.00 13.00 22.00 11.00 12.00 19.00
Check for Shear:
W = wuLS
12.02 13.36 72.47 112.47 111.11 120 101.11 OK
7.37 63.19
Kn Kn
SAFE!!!!!
Transverse Bars Top Bar
10 mm. @ 11.00 cm. oc
Bot.Bar
cm. oc //////////////
Bot.Bar 10 mm. @ cm.oc
10 mm. @ 13.00 cm. oc
10 mm. @ 22.00 cm. oc
10 mm. @ 11.00 cm. oc 10 mm. @ 12.00 cm. oc
//////////////
//////////////
//////////////
//////////////
//////////////
'///// '///// '/////
///// ///// /////
'///// '///// '///// '///// '///// '///// '///// '///// '///// '///// '/////
///// ///// ///// ///// ///// ///// ///// ///// ///// ///// ///// .
. .
. .
. .
1.5 m. Case # 1 2 3 4 5 6 7 8 9
cm. oc
L Top . . ////////////// . . . . ////////////// ////////////// . . ////////////// ////////////// //////////////
L Bottom . . ////////////// . . ////////////// ////////////// . . . . . . ////////////// . .
3 m.
S Left .
. . .
. '///// '///// '///// . . . '///// '///// '/////
S Right . . ///// ///// . . . . . . ///// ///// . . /////
. .
. .
.
1.5 m.
All Four Edges discontinues All Four Edges continues Two long edges discontinues One long one short discontinues Two short edges discontinues Two short one long edge discontinues Two long one short edges discontinues One long edge discontinues One short edge discontinues
1 m.
2 m.
1 m.
8 0.03 0.06 0.04 0.06 0.04 0.05 0.05 0.05 0.06 0.04 0.06 0.04 0.07 0.03 0.07 0.02 0.08 0.02 0.09 0.01 0.09 0.01
9 0.06 0.03 0.07 0.03 0.07 0.03 0.07 0.02 0.08 0.02 0.08 0.01 0.08 0.01 0.08 0.01 0.09 0.01 0.09 0.01 0.09 0
0.03 0.06 0.04 0.06 0.04 0.05 0.05 0.05 0.06 0.04 0.06 0.04 0.07 0.03 0.07 0.02 0.08 0.02 0.09 0.01 0.09 0.01
0.07 0.03
8 0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.01 0.04 0.01 0.04 0.01 0.05 0.01 0.05 0.01
9 0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.04 0 0.04 0
0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.01 0.04 0.01 0.04 0.01 0.05 0.01 0.05 0.01
0.04 0.01
0.06 0
0.04 0
0.06 0
8 0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
9 0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.07 0
0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
0.05 0.01
8 0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.55 0.45 0.61 0.39 0.68 0.32 0.74 0.26
9 0.67 0.33 0.71 0.29 0.75 0.25 0.79 0.21 0.83 0.17 0.86 0.14 0.9 0.11 0.92 0.08
0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.55 0.45 0.61 0.39 0.68 0.32 0.74 0.26
0.68 0.32
0.8 0.2 0.85 0.15 0.89 0.11
0.94 0.06 0.85 0.15 0.97 0.03
0.8 0.2 0.85 0.15 0.89 0.11
General Description:
DESIGN OF TWO-WAY SLAB Design Specifications: Coefficient Method: Yield Stresses: fy fc'
276 20.7
Mpa Mpa
Loading: Service Live Load Service Dead Load
2.8 2
Kpa Kpa
Slab: M Ratio L - Long span S - Short span Slab h Concrete cover
0.70
6 4 120 25 8
Slab Reinforcement: diam. Ǿ Bar Area
10 78.54
Check for Shear:
Case # 1 2 3 4 5 6 7 8 9
Excluding slab weight)
Two - way Slab
Case Number (#)
Short Direction: Long Direction: Reinforcement Ratio: 1.4/fy <ρ> 0.0051 0.01
T.B. - Transverse Bar L.B. - Longitudinal Bar Top Bar Bottom Bar Continues Edge
m. m. mm mm
=>
Min. h 111
One long edge discontinues mm mm²
L o n g i t u d i n a l B a r
Check for Effective Depth:
SAFE!!!!! SAFE!!!!!
OK OK
.75ρb 0.0278
Description All Four Edges discontinues All Four Edges continues Two long edges discontinues One long one short discontinues Two short edges discontinues Two short one long edge discontinues Two long one short edges discontinues One long edge discontinues One short edge discontinues
Philippine Standard reinforcing Bars R - Bar Area Diameter 6 mm 28.27 6 10 mm 78.54 10 12 mm 113.09 12 15 mm 176.71 15 20 mm 314.15 20 25 mm 490.86 25 28 mm 615.73 28 32 mm 804.22 32
Table. 1. COEFFICIENTS OF NEGATIVE MOMENTS IN SLABS
/////////
Top Bar 11.00
Ma, neg. = Ca, neg WLa² Mb, neg. = Cb,neg.WLb² M= 0.70 Ratio: Coef. M=La/Lb Ca, neg. 1 Cb, neg. Ca, neg. 0.95 Cb, neg. Ca, neg. 0.9 Cb, neg. Ca, neg. 0.85 Cb, neg. Ca, neg. 0.8 Cb, neg. Ca, neg. 0.75 Cb, neg. Ca, neg. 0.7 Cb, neg. Ca, neg. 0.65 Cb, neg. Ca, neg. 0.6 Cb, neg. Ca, neg. 0.55 Cb, neg. Ca, neg. 0.5 Cb, neg.
Where: W = Total dead + Live Load Case #
8
1
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0.05 0.05 0.05 0.04 0.06 0.04 0.06 0.03 0.07 0.03 0.07 0.02 0.07 0.02 0.08 0.01 0.08 0.01 0.08 0.01 0.07 0.01
Case # 5
4 0 0.08 0 0.07 0 0.07 0 0.07 0 0.06 0 0.06 0 0.05 0 0.04 0 0.04 0 0.03
0.05 0.05 0.06 0.05 0.06 0.04 0.07 0.03 0.07 0.03 0.08 0.02 0.08 0.02 0.09 0.02 0.09 0.01 0.09 0.01 0.09 0.01
0.02
6 0.08 0 0.08 0 0.08 0 0.08 0 0.08 0 0.09 0 0.09 0 0.09 0 0.09 0 0.09 0 0.09 0
7 0.07 0 0.08 0 0.08 0 0.08 0 0.09 0 0.09 0 0.09 0 0.09 0 0.1 0 0.1 0 0.1 0
0 0.07 0 0.07 0 0.06 0 0.06 0 0.05 0 0.04 0 0.04 0 0.03 0 0.02 0 0.02 0 0.01
Table. 2. COEFFICIENTS FOR DEAD - LOAD POSITIVE MOMENTS IN SLABS Ma, pos dL = Ca, dL WLa² Mb, pos,Dl. = Cb,dLWLb² M= 0.70 Case # Ratio: Coef. M=La/Lb 1 Ca, dL. 0.04 1 Cb, dL 0.04 Ca, dL. 0.04 0.95 Cb, dL 0.03 Ca, dL. 0.05 0.9 Cb, dL 0.03 Ca, dL. 0.05 0.85 Cb, dL 0.03 Ca, dL. 0.06 0.8 Cb, dL 0.02 Ca, dL. 0.06 0.75 Cb, dL 0.02 Ca, dL. 0.07 0.7 Cb, dL 0.02 Ca, dL. 0.07 0.65 Cb, dL 0.01 Ca, dL. 0.08 0.6 Cb, dL 0.01 Ca, dL. 0.09 0.55 Cb, dL 0.01
Where: W = Total uniform deadload 8 2
3 0.02 0.02 0.02 0.02 0.02 0.01 0.02 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0 0.04 0
Case # 5
4 0.02 0.03 0.02 0.03 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01
0.03 0.03 0.03 0.02 0.03 0.02 0.04 0.02 0.04 0.02 0.04 0.01 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01
6 0.03 0.02 0.03 0.02 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.04 0.01 0.04 0 0.04 0 0.04 0
7 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0
0.03 0.03 0.03 0.03 0.04 0.03 0.04 0.03 0.05 0.02 0.05 0.02 0.06 0.02 0.07 0.01 0.07 0.01 0.08 0.01
0.5
Ca, dL. Cb, dL
0.1 0.01
0.04 0
0.08 0.01
0.06 0
0.04 0
0.06 0
0.09 0.01
Table. 3. COEFFICIENTS FOR LIVE - LOAD POSITIVE MOMENTS IN SLABS Ma, pos, LL = Ca, LL WLa² Mb, pos,LL. = Cb,LLWLb² M= 0.70 Case # Ratio: Coef. M=La/Lb 1 Ca, dL. 0.04 1 Cb, dL 0.04 Ca, dL. 0.04 0.95 Cb, dL 0.03 Ca, dL. 0.05 0.9 Cb, dL 0.03 Ca, dL. 0.05 0.85 Cb, dL 0.03 Ca, dL. 0.06 0.8 Cb, dL 0.02 Ca, dL. 0.06 0.75 Cb, dL 0.02 Ca, dL. 0.07 0.7 Cb, dL 0.02 Ca, dL. 0.07 0.65 Cb, dL 0.01 Ca, dL. 0.08 0.6 Cb, dL 0.01 Ca, dL. 0.09 0.55 Cb, dL 0.01 Ca, dL. 0.1 0.5 Cb, dL 0.01
Where: W = Total uniform Liveload 8 2
3 0.03 0.03 0.03 0.03 0.03 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.07 0
Case # 5
4 0.03 0.03 0.03 0.03 0.04 0.03 0.04 0.02 0.05 0.02 0.05 0.02 0.06 0.02 0.06 0.01 0.07 0.01 0.08 0.01 0.09 0.01
0.03 0.03 0.04 0.03 0.04 0.03 0.04 0.02 0.05 0.02 0.05 0.02 0.06 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
6 0.03 0.03 0.03 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.04 0.01 0.07 0
7 0.04 0.03 0.04 0.03 0.04 0.03 0.46 0.02 0.05 0.02 0.06 0.02 0.06 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
0.03 0.04 0.04 0.03 0.04 0.03 0.05 0.03 0.05 0.02 0.06 0.02 0.06 0.02 0.07 0.01 0.08 0.01 0.09 0.01 0.09 0.01
Table. 4. RATIO OF LOAD w in La and Lb DIRECTIONS FOR SHEAR IN SLAB AND LOAD IN SUPPORTS M= Ratio: M=La/Lb 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65
0.70 Coef. Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb Wa Wb
Case #
8
1
2 0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
3 0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
Case # 5
4 0.17 0.83 0.2 0.8 0.23 0.77 0.28 0.72 0.33 0.67 0.39 0.61 0.45 0.55 0.53 0.47
0.5 0.5 0.55 0.45 0.6 0.4 0.66 0.34 0.71 0.29 0.76 0.24 0.81 0.19 0.85 0.15
6 0.83 0.17 0.86 0.14 0.88 0.12 0.9 0.1 0.92 0.08 0.94 0.06 0.95 0.05 0.96 0.04
7 0.71 0.29 0.75 0.25 0.79 0.21 0.83 0.17 0.86 0.14 0.88 0.12 0.91 0.09 0.93 0.07
0.29 0.71 0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.56 0.44 0.62 0.38 0.69 0.31
0.6 0.55 0.5
Wa Wb Wa Wb Wa Wb
0.89 0.11 0.92 0.08 0.94 0.06
0.89 0.11 0.92 0.08 0.94 0.06
0.61 0.39 0.69 0.31 0.76 0.24
0.89 0.11 0.92 0.08 0.94 0.06
0.97 0.03 0.98 0.02 0.99 0.01
0.95 0.05 0.96 0.04 0.97 0.03
0.76 0.24 0.81 0.19 0.86 0.14
Solution: Slab Weight:
2,825.28 2.83 4.83 2.80
Deadload: Liveload Wu = 1.4Wd + 1.7WL Total Load, Wu = M = La/Lb Considering 1 meter strip:
11.52
N/mm² Kpa Kpa Kpa Kpa
0.70 11.52 Kn/m
AT SHORT DIRECTION: Negative Moment at Continues Edges (Top Bars) Ca, neg. 0.07 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 0.05 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. 0.03 Mb, neg. = Cb, neg WLb² 12.02 Kn-m Positive Moment at Midspan (Bottom Bars) Deadload, Cb 0.01 Ma, pos, dL = CbWLb² 2.68 Kn-m Liveload, Cb 0.05 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
ρmin. = 1.4/fy ρmax = .75(β)²(fc'/fy)(600/(600+fy)) ρ (Selected) m = fy/.85fc' Rn = ρfy(1-ρm/2)
SHORT SPAN LONG SPAN Cont. Edge Midspan Discont.Edge Cont. Edge Midspan Discont.Edge 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.01 0.01 0.01 0.01 0.01 0.01 15.686 15.686 15.686 15.686 15.686 15.686 2.544 2.544 2.544 2.544 2.544 2.544
Max. Ultimate Moment Mu = Mn = Mu/.9 Req. d = sqrt(Mn/bRn), mm Req. h = d+1/2bar dia.+bar dia.+cover Min. h = 2(L+S)*1000/180 Actual h = Effective d = h - (bar dia. + 1/2 bar dia)
Max. Ultimate Moment, Mu = Mn = Mu/.90 Rn = Mn/bd² ρmin. = 1.4/fy ρmax = .75(β)²(fc'/fy)(600/(600+fy)) ρ = 1/m(1 - sqrt(1-2mRn/fy) As = ρbd Reinf. Bar diameter, mm Reinf. Bar Spacing, mm Min. Spacing, 3h Final Bar Spacing, cm.
12.53 13.92 73.98 113.98 111.11 120 96.11 OK
8.44 9.37 60.71 100.71 111.11 120 101.11 OK
2.81 3.12 35.05 75.05 111.11 120
Load on Supporting Beams: 276.37
Kn
0.68 187.93
Kn
Short Direction: Wa = Shear ratio on slab Ws = Wa*wu Load per meter on short beam, Ws/2S ØVc = .85(.17)(√fc')(Eff. d)
23.49
Kn
66.47
Kn
0.32 88.44
Kn
SAFE!!!!!
Long Direction: Wb = Shear ratio on slab WL = Wb*wu Load per meter on short beam, Wb/2L ØVc = .85(.17)(√fc')(Eff. d)
9.25 10.28 63.58 103.58 111.11 120 96.11 OK
3.98 4.42 41.68 81.68 111.11 120
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 12.53 8.44 2.81 12.02 9.25 3.98 13.92 9.37 3.12 13.36 10.28 4.42 2.544 2.544 2.544 2.544 2.544 2.544 0.0051 0.0051 0.0051 0.0051 0.0051 0.0051 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.01 0.01 0.01 0.01 0.0100 0.01 739.800 607.059 350.486 724.686 635.787 416.768 10 10 10 10 10 10 106.16 129.38 224.09 108.38 123.53 188.45 341.94 302.12 225.15 337.41 310.74 245.03 11.00 13.00 22.00 11.00 12.00 19.00
Check for Shear:
W = wuLS
12.02 13.36 72.47 112.47 111.11 120 101.11 OK
7.37 63.19
Kn Kn
SAFE!!!!!
Transverse Bars Top Bar
10 mm. @ 11.00 cm. oc
Bot.Bar
cm. oc //////////////
Bot.Bar 10 mm. @ cm.oc
10 mm. @ 13.00 cm. oc
10 mm. @ 22.00 cm. oc
10 mm. @ 11.00 cm. oc 10 mm. @ 12.00 cm. oc
//////////////
//////////////
//////////////
//////////////
//////////////
'///// '///// '/////
///// ///// /////
'///// '///// '///// '///// '///// '///// '///// '///// '///// '///// '/////
///// ///// ///// ///// ///// ///// ///// ///// ///// ///// ///// .
. .
. .
. .
1.5 m. Case # 1 2 3 4 5 6 7 8 9
cm. oc
L Top . . ////////////// . . . . ////////////// ////////////// . . ////////////// ////////////// //////////////
L Bottom . . ////////////// . . ////////////// ////////////// . . . . . . ////////////// . .
3 m.
S Left .
. . .
. '///// '///// '///// . . . '///// '///// '/////
S Right . . ///// ///// . . . . . . ///// ///// . . /////
. .
. .
.
1.5 m.
All Four Edges discontinues All Four Edges continues Two long edges discontinues One long one short discontinues Two short edges discontinues Two short one long edge discontinues Two long one short edges discontinues One long edge discontinues One short edge discontinues
1 m.
2 m.
1 m.
8 0.03 0.06 0.04 0.06 0.04 0.05 0.05 0.05 0.06 0.04 0.06 0.04 0.07 0.03 0.07 0.02 0.08 0.02 0.09 0.01 0.09 0.01
9 0.06 0.03 0.07 0.03 0.07 0.03 0.07 0.02 0.08 0.02 0.08 0.01 0.08 0.01 0.08 0.01 0.09 0.01 0.09 0.01 0.09 0
0.03 0.06 0.04 0.06 0.04 0.05 0.05 0.05 0.06 0.04 0.06 0.04 0.07 0.03 0.07 0.02 0.08 0.02 0.09 0.01 0.09 0.01
0.07 0.03
8 0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.01 0.04 0.01 0.04 0.01 0.05 0.01 0.05 0.01
9 0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.03 0.01 0.04 0 0.04 0
0.02 0.02 0.02 0.02 0.03 0.02 0.03 0.02 0.03 0.02 0.04 0.01 0.04 0.01 0.04 0.01 0.05 0.01 0.05 0.01
0.04 0.01
0.06 0
0.04 0
0.06 0
8 0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
9 0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.01 0.05 0.01 0.05 0.01 0.06 0.01 0.06 0.01 0.07 0
0.03 0.03 0.03 0.03 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.01 0.06 0.01 0.07 0.01 0.07 0.01 0.08 0.01
0.05 0.01
8 0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.55 0.45 0.61 0.39 0.68 0.32 0.74 0.26
9 0.67 0.33 0.71 0.29 0.75 0.25 0.79 0.21 0.83 0.17 0.86 0.14 0.9 0.11 0.92 0.08
0.33 0.67 0.38 0.62 0.43 0.57 0.49 0.51 0.55 0.45 0.61 0.39 0.68 0.32 0.74 0.26
0.68 0.32
0.8 0.2 0.85 0.15 0.89 0.11
0.94 0.06 0.85 0.15 0.97 0.03
0.8 0.2 0.85 0.15 0.89 0.11
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