SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date: All units are in Newtons and meters unless otherwise indicated
A
Llong
B
Dshort
Dlong
Lshort
1
Corner Slab
Lshort
2
Edge Slab 1
Short Direction
3
The following are the assumptions of this worksheet: 1. All spans (long and short direction) are uniform length. 2. All columns have uniform dimensions (long and short direction). 3. There may or may not be any overhang (D long and/or D short may or may not be zero) 4. There may or may not be any wall load (W wall may or may not be zero). 5. Slab is of uniform thickness. 6. Direct design method is applicable. Fixed inputs: Span in long direction, Llong =
Clear span in long direction Lnlong = Llong-clong = Overhang in long direction, Dlong = Span in short direction, Lshort = Clear span in short direction, Lnshort = Lshort-cshort = Overhang in short direction, Dshort = Column width in long direction, clong =
426.409.3.2.1
Column width in short direction, cshort = Floor to floor height, H = Capacity reduction factor for flexure fb =
426.409.3.2.3
Capacity reduction factor for shear fv = Live load, wLL = Superimposed dead load: Floor finish, waterproofing, etc., wDL1 = Other dead loads, wDL2 = Exterior wall load, Wwall (N/m) =
426.409.2.1
204-1
Load Factor for Dead Load, LFDL = Load Factor for Live Load, LFLL = Design inputs: Slab thickness, t = Unit weight of concrete gconc = Concrete strength, f'c = Steel yield strength, fy = m= fy/0.85*f'c =
Page 1 of 6
Llong
C
Long Direction
Edge Slab 2
cshort clong
Interior Slab
/or D short may or may not be zero) or may not be zero).
7.200
6.750 0.000 7.200 6.750 0.000 0.450 0.450 4.500 0.900 0.850 4,800 3,120 1,200 7,800 1.40 1.70 0.180 23,600 12,860,000 309,000,000 28.268
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date: 409.6.3.2
Minimum slab thickness:
Table 409-3 Yield Strength 280,000,000 309,000,000 415,000,000 N.A. 520,000,000
Minimum slab thickness Exterior Panels Interior Panels 0.205 0.188 0.209 0.191 0.225 0.205 0.000 0.000 0.241 0.218
Minimum thickness, exterior panel, tminext = Minimum thickness, interior panel, tminint = Minimum thickness, tmin = smaller of tminext or tminint = Capacity/Demand Ratio for Slab Thickness = t/tmin = Uniform load on slab: Dead Load: Slab weight, wDLslab = t*gconc = Floor finish, waterproofing, etc., wDL1 = Other dead loads, wDL2 = wDL = wDLslab+wDLothers = Live Load = Total load, wtotal = LFLL*wLL+LFDL*wDL =
413.7.1.1 413.7.1.2 413.7.1.3 413.7.1.4 413.7.1.5 413.7.1.5 413.7.1.6
Direct design method criteria: 1. There are a minimum of three continous spans in each direction. 2. Panels are rectangular, with ratio of longer to shorter span center-to-center support within panel not greater than 2. 3. Successive span lengths center-to-center supports in each direction do not differ by more one-third the longer span. 4. Offsets of columns are a minimum of 10% of the span in direction of offset from either ax between center lines of successive columns. 5. All loads shall be due to gravity loads only and distributed over the entire panel. 6. Live load shall not exceed two times the dead load. 7. The relative stiffness of beams in two perpendicular directions (af1*L22)/af2*L12) shall not be less than 0.2 nor greater than 5.0.
orter span center-to-center support within a
ts in each direction do not differ by more than
e span in direction of offset from either axis
istributed over the entire panel.
Page 2 of 6
0.209 0.191 0.191 0.94
4,248 3,120 1,200 8,568 4,800 20,155
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date: All units are in Newtons and meters unless otherwise indicated Moment analysis: Slab strips in long direction:
A
B
C
Column strip 1 Half middle strip
Half middle strip Column strip 2
Half middle strip
Short Direction
3
Slab strips in short direction:
A
C
B
1
Half middle strip
Column strip
Half middle strip
Half middle strip
3
Column strip
2
Short Direction
Half middle strip
Column strip
Half middle strip
Half middle strip
Column strip
3
Page 1 of 6
Dshort
C
0.5*Lshort
0.5*cshort
Lshort
0.50*Lshort+ 0.5*cshort+Dshort
C
Long Direction
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date: 413.7.2.2
Total factored static moment: Slab strips in long direction: 2 Slab strip 1: Mo1 = wtotal*(0.5*Lshort+0.5*cshort+Dshort)*Lnlong /8 = Slab strip 2: Mo2 = wtotal*Lshort*Lnlong2/8 = Slab strips in short direction: Slab strip A: MoA = wtotal*(0.5*Llong+0.5*clong*Dlong)*Lnshort2/8 = 2
Slab strip B: MoB = wtotal*Llong*Lnshort /8 = Wall load: In long direction: Mow1 = LFDL*Wwall*Lnlong2/8 = 413.7.3.3
In short direction: MowA = LFDL*Wwall*Lnshort2/8 = Calculation of longitudinal moments
Mo -M at exterior support +M at exterior span -M at first interior support -M at typical interior support +M at typical interior support 413.7.4.2
0.26*Mo 0.52*Mo 0.70*Mo 0.65*Mo 0.35*Mo
Frame 1 Mo1
Frame 2 Mo2
439,072
826,489
114,159 228,318 307,351 285,397 153,675
214,887 429,774 578,542 537,218 289,271
Percentage of exterior negative moment going to column strip: Frames 1 and 2:
Frames A and B: L2/L1 1.000
1.000
99.07% 75.00%
100.00% 99.07% 75.00%
0.500 bt = 0 100.00% 0.09 99.07% b t > 2.5 75.00%
Column strip %, exterior negative moment a1 a1*(L2/L1) C
L2/L1 Frames 1 & 2 Frames A & B
1.000 1.000
0.000 0.000
Torsional constant C: In long direction: cshort t In short direction: clong c
bt = 0 0.09 b t > 2.5
0.000 0.000
0.00065 0.00065
Clong = (1-0.63*t/cshort)*(t3*cshort/3) =
t
3
Cshort = (1-0.63*t/clong)*(t *clong/3) =
clong c
t
413.7.4.1
Percentage of interior negative moments going to column strip =
413.7.4.4
Percentage of positive moment going to column strip = Moments in column strip and middle strip slabs: Total moment Frame 1
Exterior span
Interior span Frame 2
Exterior span
Interior span Frame A
Exterior span
Interior span Frame B
Exterior span
Interior span
-Mext +M -Mint -M +M -Mext +M -Mint -M +M -Mext +M -Mint -M +M -Mext +M -Mint -M +M
114,159 228,318 307,351 285,397 153,675 214,887 429,774 578,542 537,218 289,271 114,159 228,318 307,351 285,397 153,675 214,887 429,774 578,542 537,218 289,271
% momnt to column strip slab 99.07% 60.00% 75.00% 75.00% 60.00% 99.07% 60.00% 75.00% 75.00% 60.00% 99.07% 60.00% 75.00% 75.00% 60.00% 99.07% 60.00% 75.00% 75.00% 60.00%
rt+Dshort)*Lnlong
2
/8 =
439,072.37 826,489.17
*Dlong)*Lnshort2/8 =
439,072.37 826,489.17 62,192.81 62,192.81
Frame A MoA
Frame B MoB
Wall 1 MoW1
Wall A MoWA
439,072
826,489
62,193
62,193
114,159 228,318 307,351 285,397 153,675
214,887 429,774 578,542 537,218 289,271
16,170 32,340 43,535 40,425 21,767
16,170 32,340 43,535 40,425 21,767
L2/L1 1.000
2.000
Frames A and B: 1.000
100.00% 100.00% 99.07% 99.07% 99.07% 75.00% 75.00% 75.00%
rior negative moment Is
bt
%
0.00350 0.00350
0.094 0.094
99.07% 99.07%
t/cshort)*(t3*cshort/3) = 3
*t/clong)*(t *clong/3) =
0.00065 0.00065
75.00% 60.00%
Moment in column strip slab wall 113,091 16,170 136,991 32,340 230,513 43,535 214,048 40,425 92,205 21,767 212,878 257,865 433,907 402,913 173,563 113,091 16,170 136,991 32,340 230,513 43,535 214,048 40,425 92,205 21,767 212,878 257,865 433,907 402,913 173,563
Moment Moment in column in middle strip slab strip slab 129,262 1,067 169,331 91,327 274,048 76,838 254,473 71,349 113,973 61,470 212,878 2,009 257,865 171,910 433,907 144,636 402,913 134,304 173,563 115,708 129,262 1,067 169,331 91,327 274,048 76,838 254,473 71,349 113,973 61,470 212,878 2,009 257,865 171,910 433,907 144,636 402,913 134,304 173,563 115,708
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date:
Shear analysis: Edge column B1:
B a
b
W 1
Z
Z c
Centroid of shear perimeter
d
W
Short direction
a3 = clong+t
a1 a2 a3 a4 a5
0.56*Llong a1 = 1.06*Llong
1.06*Llong = Dshort+0.5*cshort+0.44*Lshort = clong+t = Dshort+cshort+0.5*t = (Aac*0.5*a4+Abd*0.5*a4)/(Acd+Aac+Abd) = Aac = Abd = a4*t = Acd = a3*t = a6 = 0.5*a4-a5 =
411.13.2.1
= = = = =
Shear capacity f*Vc: bo = 2*a4+a3 = Vc1 = (1/6)*[1+2/(clong/cshort)]*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc2 = (1/12)*(as*t/b0+2)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = For edge column, as = 30 Vc3 = (1/3)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc = smallest of Vc1, Vc2 or Vc3 = C fv*Vc = fv*vc = fv*Vc/(bo*t) =
Direct shear due to slab and wall loads, Vudirect: Vuslab = wtotal*[(a1*a2-a3*a4] = Vuwall = LFDL*Wwall*(a1-a3) = Vudirect = Vuslab+Vuwall = Vudirect/(fv*Vc) = Direct shear stress due to slab and wall loads, vudirect: vudirecta = vudirectb = vudirectc = vudirectd = Vudirect/(bo*t) = Moment about axis Z-Z to be transferred to the column: 413.7.3.6
The gravity load moment to be transferred between slab and edge column shall be 0.3 MZZ = 0.30*MoB =
413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be tra gfZZ1 = 1/[1+(2/3)*sqrt(a4/a3)]
413.6.3.3
For edge columns with unbalanced moments about an axis parallel to the edge, g f = V u at an edge support does not exceed 0.75* f v *V c gfZZ = gfaZZ1 if Vudirect/(fv*Vc)>0.75; gfZZ = 100% if Vudirect/(fv*Vc)<0.75
413.6.3.2
Capacity/Demand Ratio for flexure, moment about axis Z-Z: Moment be transferred by flexure MZZb = gfZZ*Mzz = Effective width for flexure = beff = clong+3*t = Moment capacity Mcap = beff*MCSshort = C/D Ratio in bending = Mcap/MZZb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis Z-Z transferred by shear: Moment to be transferred by shear MZZv = (1-gfZZ)*Mzz = vuZZc = vuZZd = MZZv*a5/JZZ = vuZZa = vuzzb = -Mzzv*(a4-a5)/JZZ = JZZ = Jac+Jbd+Jcd = Jac = Jbd = Ixac+Iyac = Ixac = a4*t3/12 = Iyac = a43*t/12+(a4*t)*a62 = Jcd = (a3*t)*a52 =
Moment about axis W-W to be transferred to the column (from column line 1 wit Unbalanced moment from slab, MWWslab: Negative moment at first interior support M1 = 0.70*Mo1 = Negative moment at typical interior support M2 = 0.65*M01 = Negative moment at typical interior support, dead load only, M3 = (LFDL*w MWWslab = M1-M3 = Unbalanced moment from wall, MWWwall: Negative moment at first interior support M1 = 0.70*Mow1 = Negative moment at typical interior support M2 = 0.65*Mow1 = MWWwall = M1-M2 = MWW = MWWslab+MWWwall = 413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be tra gfaWW = 1/[1+(2/3)*sqrt(a3/a4)]
413.6.3.3
For edge columns with unbalanced moments about an axis transverse to the edge, inc 1.25 times the value but not more than 1.0 provided that V u at the support does not
Percentage of moment transferred by flexure, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25 Capacity/Demand Ratio for flexure, moment about axis W-W: Moment be transferred by flexure MWWb = gfWW*MWW =
Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort cshort+3*t = cshort+1.5*t+Dshort = Moment capacity Mcap = beff*MCSlong = C/D Ratio = Mcap/MWWb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis W-W transferred by shear: Moment to be transferred by shear MWWv = (1-gfWW)*MWW = vuWWa = vuWWc = MWWv*0.5*a3/JWW = vuWWb = vuWWd = -vuWWa = Jww = Jcd+Jac+Jbd = Jcd = Ixcd+Iycd = 3 Ixcd = a3*t /12 = 3 Iycd = a3 *t/12 = 2 Jac = Jbd = a4*t*(0.5*a3) = Shear stresses: vua = vudirecta+vuZZa+vuWWa = vub = vudirectb+vuZZv+vuWWb = vuc = vudirectc+vuZZc+vuWWc = vud = vudirectd+vuZZd+vuWWd = Critical shear stress: vu = largest of absolute values of vua, vub, vuc or vud = Capacity/Demand Ratio for shear: C/D Ratio = fv*vc/vu = Slab adequate in shear if C/D ratio > 1.0
Page 6 of 6
000)*bo*t*1,000,000 = *bo*t*1,000,000 =
0.44*Lshort
0.5*cshort
a2 = 0.44*Lshort+0.5*cshort+Dshort
0.50*Llong
a4 = 0.5*t+cshort+Dshort
0.5*a4
Z
a5
a6
Dshort
Long direction
7.632 3.393 0.630 0.540 0.171 0.097 0.113 0.099
1.71 551,898.36 474,438.94 474,438.94 367,932.24 367,932.24 312,742.40 1,016,057.19
515,069.68 76,461.84 591,531.52 1.89 1,921,804.82
etween slab and edge column shall be 0.3*M o . 247,946.75
n by g f *M u shall be considered to be transferred by flexure 61.83%
about an axis parallel to the edge, g f = 1.0 provided that
% if Vudirect/(fv*Vc)<0.75
61.83%
about axis Z-Z: 153,317.27 0.99 0.00 Not adequate
ransferred by shear: 94,629.48 1,541,246.89 -3,339,368.25 0.01047 0.00359 0.00026 0.00332 0.00330
o the column (from column line 1 with LL on span A-B only):
rt M1 = 0.70*Mo1 = pport M2 = 0.65*M01 = or support, dead load only, M3 = (LFDL*wDL/wtotal)*M2 =
307,351 285,397 169,852 137,499
rt M1 = 0.70*Mow1 = pport M2 = 0.65*Mow1 =
43,535 40,425 3,110 140,609
n by g f *M u shall be considered to be transferred by flexure 58.14%
about an axis transverse to the edge, increase g f to as much as provided that V u at the support does not exceed 0.40* f v *V c .
, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40
58.14%
about axis W-W: 81,745.29
cshort+3*t or cshort+1.5*t+Dshort
0.720 0.990 0.720 0.00 Not adequate
W transferred by shear: 58,863.33 794,216.20 -794,216.20 0.02335 0.00406 0.00031 0.00375 0.00964 -623,347.23 -2,211,779.64 -2211780 4,257,267.91 4257267.9 2,668,835.50 4,257,267.91 0.24 Not adequate
Critical section
0.50*Lshort
0.50*L
Critical section
0.56*Lshort
0.56*Llong-0.5*clong-dave
clong+dave
0.50*Lshort
clong+dave Critical Section 0.56*Llong
0.50*Lshort
cshort+dave 0.50*Llong
0.56*Lshort
Llong
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date: Edge column A2:
A
Z
a6
a3 = cshort+t
Z
c
a
2
W
W
b
d
Centroid of shear perimeter
Long direction
a5
Short direction
0.5*a4 a4 = Dlong+clong+0.5*t
Dlong 0.5*clong
0.44*Llong
a2 = Dlong+0.5*clong+0.44*Llong
a1 a2 a3 a4 a5
1.06*Lshort = Dlong+0.5*clong+0.44*Llong = cshort+t = Dlong+clong+0.5*t = (Aac*0.5*a4+Abd*0.5*a4)/(Acd+Aac+Abd) = Aac = Abd = a4*t = Acd = a3*t = a6 = 0.5*a4-a5 =
411.13.2.1
= = = = =
Shear capacity f*Vc: bo = 2*a4+a3 = Vc1 = (1/6)*[1+2/(clong/cshort)]*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc2 = (1/12)*(as*t/b0+2)*sqrt(f'c/1,000,000)*bo*t*1,000,000 =
For edge column, as = 30 Vc3 = (1/3)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc = smallest of Vc1, Vc2 or Vc3 = fv*Vc = fv*vc = fv*Vc/(bo*t) = Direct shear due to slab and wall loads, Vudirect: Vuslab = wtotal*[(a1*a2-a3*a4] = Vuwall = LFDL*Wwall*(a1-a3) = Vudirect = Vuslab+Vuwall = Vudirect/(fv*Vc) = Direct shear stress due to slab and wall loads, vudirect: vudirecta = vudirectb = vudirectc = vudirectd = Vudirect/(bo*t) = Moment about axis Z-Z to be transferred to the column: 413.7.3.6
The gravity load moment to be transferred between slab and edge column shall be 0.3*M o . MZZ = 0.30*Mo2 =
413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be transferr gfZZ1 = 1/[1+(2/3)*sqrt(a4/a3)]
413.6.3.3
For edge columns with unbalanced moments about an axis parallel to the edge, g f = 1.0 pr V u at an edge support does not exceed 0.75* f v *V c gfZZ = gfaZZ1 if Vudirect/(fv*Vc)>0.75; gfZZ = 100% if Vudirect/(fv*Vc)<0.75
413.6.3.2
Capacity/Demand Ratio for flexure, moment about axis Z-Z: Moment be transferred by flexure MZZb = gfZZ*Mzz = Effective width for flexure = beff = clong+3*t = Moment capacity Mcap = beff*MCSshort = C/D Ratio in bending = Mcap/MZZb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis Z-Z transferred by shear: Moment to be transferred by shear MZZv = (1-gfZZ)*Mzz = vuZZc = VuZZd = MZZv*a5/JZZ = vuZZa = VuZZb = -Mzzv*(a4-a5)/JZZ = JZZ = Jac+Jbd+Jcd = Jac = Jbd = Ixac+Iyac = Ixac = a4*t3/12 = 3 2 Iyac = a4 *t/12+(a4*t)*a6 = 2 Jcd = (a3*t)*a5 =
Moment about axis W-W to be transferred to the column (from column line A with LL Unbalanced moment from slab, MWWslab: Negative moment at first interior support M1 = 0.70*MoA = Negative moment at typical interior support M2 = 0.65*M0A = Negative moment at typical interior support, dead load only, M3 = (LFDL*wDL/wto MWWslab = M1-M3 = Unbalanced moment from wall, MWWwall: Negative moment at first interior support M1 = 0.70*MowA = Negative moment at typical interior support M2 = 0.65*MowA = MWWwall = M1-M2 = MWW = MWWslab+MWWwall = 413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be transferr gfaWW = 1/[1+(2/3)*sqrt(a3/a4)]
413.6.3.3
For edge columns with unbalanced moments about an axis transverse to the edge, increase 1.25 times the value but not more than 1.0 provided that V u at the support does not excee
Percentage of moment transferred by flexure, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW Capacity/Demand Ratio for flexure, moment about axis W-W: Moment be transferred by flexure MWWb = gfWW*MWW = Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort cshort+3*t = cshort+1.5*t+Dshort = Moment capacity Mcap = beff*MCSlong = C/D Ratio = Mcap/MWWb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis W-W transferred by shear: Moment to be transferred by shear MWWv = (1-gfWW)*MWW = vuWWb = vuWWd = MWWv*0.5*a3/JWW = vuWWa = vuWWc = -MWWv*0.5*a3/JWW = Jww = Jcd+Jac+Jbd = Jcd = Ixcd+Iycd = Ixcd = a3*t3/12 = Iycd = a33*t/12 = Jac = Jbd = a4*t*(0.5*a3)2 = Shear stresses: vua = vudirecta+vuZZa+vuWWa = vub = vudirectb+vuZZb+vuWWb = vuc = vudirectc+vuZZc+vuWWc = vud = vudirectd+vuZZd+vuWWd = Critical shear stress: vu = largest of vua, vub, vuc or vud = Capacity/Demand Ratio for shear: C/D Ratio = fv*vc/vu = Slab adequate in shear if C/D ratio > 1.0
Page 6 of 6
a1 = 1.06*Lshort
0.50*Lshort
0.56*Lshort
Long direction
7.632 3.393 0.630 0.540 0.171 0.097 0.113 0.099
1.71 551,898.36 474,438.94 474,438.94
30 367,932.24 367,932.24 312,742.40 1,016,057.19 515,069.68 76,461.84 591,531.52 1.89 1,921,804.82
n slab and edge column shall be 0.3*M o . 247,946.75
g f *M u shall be considered to be transferred by flexure 61.83%
t an axis parallel to the edge, g f = 1.0 provided that
udirect/(fv*Vc)<0.75
61.83% 153,317.27 0.99 0.00 Not adequate 9,038,176.19 147,206,361.56 -318,947,116.71 0.01047 0.00359 0.00026 0.00332 0.00330
column (from column line A with LL on span 1-2 only):
pport, dead load only, M3 = (LFDL*wDL/wtotal)*M2 =
307,351 285,397 169,852 137,499 43,535 40,425 3,110 140,609
g f *M u shall be considered to be transferred by flexure 58.14%
t an axis transverse to the edge, increase g f to as much as ed that V u at the support does not exceed 0.40* f v *V c . = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40
+3*t or cshort+1.5*t+Dshort
58.14% 81,745.29 0.720 0.990 0.720 0.00 Not adequate
sferred by shear: 58,863.33 794,216.20 -794,216.20 0.02335 0.00406 0.00031 0.00375 0.00964 -317,819,528.09 -316,231,095.69 -3.18E+08 148,333,950.18 -3.18E+08 149,922,382.58 -317,819,528.09 0.00 Not adequate
0.50*Lshort
Critical section
0.56*Lshort
0.56*Llong-0.5*clong-dave
clong+dave
Critical Section 0.56*Llong
0.50*Lshort
cshort+dave 0.50*Llong
0.56*Lshort
Llong
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date:
Interior column B2:
B
W a
Z
Z c
d
W
a4 = cshort+t
2
b
Short direction
a3 = clong+t
a1 a2 a3 a4
411.13.2.1
= = = =
0.50*Llong
0.56*Llong
a1 = 1.06*Llong 1.06*Llong = 1.06*Lshort = clong+t = cshort+t =
Shear capacity f*Vc: bo = 2*(a3+a4) = Vc1 = (1/6)*[1+2/(clong/cshort)]*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc2 = (1/12)*(as*t/b0+2)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = For interior column as = 40 Vc3 = (1/3)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc = smallest of Vc1, Vc2 or Vc3 = fv*Vc = fv*vc = fv*Vc/(bo*t) = Direct shear due to slab loads, Vudirect: Vudirect = wtotal*[(a1*a2-a3*a4] = Vudirect/(fv*Vc) = Direct shear stress due to slab and wall loads, vudirect:
vudirecta = vudirectb = vudirectc = vudirectd = Vudirect/(bo*t) =
Moment about axis Z-Z to be transferred to the column (from column line B with LL on Negative moment at first interior support, M1 = 0.70*MoB = Negative moment at typical interior support, M2 = 0.65*MoB = Negative moment at typical interior support, dead load only, M3 = (LFDL*wDL/wtotal)*M2 MZZ = M1-M3 = 413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be transferr gfZZ = 1/[1+(2/3)*sqrt(a4/a3)]
413.6.3.2
Capacity/Demand Ratio for flexure, moment about axis Z-Z: Moment be transferred by flexure MZZf = gfZZ*Mzz = Effective width for flexure = beff = clong+3*t = Moment capacity Mcap = beff*MCSshort = Capacity/Demand Ratio = Mcap/MZZb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis Z-Z transferred by shear: Moment to be transferred by shear MZZv = (1-gfZZ)*Mzz = vuZZa = vuZZb = MZZv*0.5*a4/JZZ = vuZZc = vuZZd = -vuZZa = JZZ = Jac+Jbd+Jab+Jcd = Jac = Jbd = Ixac+Iyac = Ixac = a4*t3/12 = Iyac = a43*t/12 = Jab = Jcd = (a3*t)*(0.5*a4)2 =
413.6.3.2
Moment about axis W-W to be transferred to the column (from column line 2 with LL Negative slab moment at first interior support M1 = 0.70*Mo2 = Negative slab moment at typical interior support M2 = 0.65*Mo2 = Negative slab moment at typical interior support, dead load only M3 = (LFDL*wDL/wtotal MWW = M1-M3 = gfWW = 1/[1+(2/3)*sqrt(a3/a4)] Capacity/Demand Ratio for flexure, moment about axis W-W: Moment be transferred by flexure MWWb = gfWW*MWW = Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort cshort+3*t = cshort+1.5*t+Dshort = Moment capacity Mcap = beff*MCSlong = Capacity/Demand Ratio = Mcap/MWWb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis W-W transferred by shear: Moment to be transferred by shear MWWv = (1-gfWW)*MWW = vuWWa = vuWWc = MWWv*0.5*a3/JWW = vuWWb = vuWWd = -vuWWa = JWW = Jac+Jbd+Jab+Jcd = Jac = Jbd = (a4*t)*(0.5*a3)2 = Jab = Jcd = Ixab+Iyab = Ixab = a3*t3/12 = 3 Iyab = a3 *t/12 = Shear stresses: vua = vudirecta+vuZZa+vuWWa =
vub = vudirectb+vuZZb+vuWWb = vuc = vudirectc+vuZZc+vuWWc = vud = vudirectd+vuZZd+vuWWd = Critical shear stress: vu = largest of absolute values of vua, vub, vuc or vud = Capacity/Demand Ratio for shear: C/D Ratio for shear = fv*vc/vu = Slab adequate in shear if C/D ratio > 1.0
Page 6 of 6
0.50*Lshort
a4 = cshort+t
a2 = 1.06*Lshort
0.56*Lshort
Long Direction
0.50*Llong
7.632 7.632 0.630 0.630
2.52 813,323.90 658,405.06 658,405.06 40 542,215.93 542,215.93 460,883.54 1,016,057.19 1,165,988.88 2.53
2,570,522.23
olumn (from column line B with LL on span 1-2 only):
dead load only, M3 = (LFDL*wDL/wtotal)*M2 =
578,542.42 537,217.96 319,720.81 338,751.81
g f *M u shall be considered to be transferred by flexure 60.00% 203,251.09 0.990 0.00 Not adequate 135,500.72 1,394,040.38 -1,394,040.38 0.03061800 0.00406 0.00031 0.00375 0.01125
column (from column line 2 with LL on span A-B only):
port, dead load only M3 = (LFDL*wDL/wtotal)*M2 =
+3*t or cshort+1.5*t+Dshort
578,542 537,218 319,721 258,822 60.00% 155,292.97 0.720 0.990 0.720 0.00 Not adequate
sferred by shear: 103,528.64 1,065,109.50 -1,065,109.50 0.03062 0.01125 0.00406 0.00031 0.00375 5,029,672.10
233805.4
2,899,453.10 5029672.1 2,241,591.35 5029672.1 111,372.35 5,029,672.10 0.20 Not adequate
0.56*L
0.50*Lshort
Critical section
0.56*Lshort
0.56*Llong-0.5*clong-dave
clong+dave
Critical Section 0.56*Llong
0.50*Lshort
cshort+dave 0.50*Llong
0.56*Lshort
Llong
SLAB DESIGN WORKSHEET Two-Way Post-Tensioned Flat Plate (slab without beams) Project: Designer: Date:
Corner column A1: A
Centroid of shear perimeter
Z
c
d
Z
0.5*a4
1
a7 a8
b a4 = 0.5*t+cshort +Dshort
a12 = Dshort+cshort+a9
W a
W a6
a5
0.5*a3 a3 = Dlong+clong+0.5*t
Two-way shear
Short direction
Dlong 0.5*clong
0.44*Llong
a1 = Dlong+0.5*clong+0.44*Llong
a1 = Dlong+0.5*clong+0.44*Llong = a2 = 0.44*Lshort+0.5*cshort+Dshort = a3 = Dlong+clong+0.5*t = a4 = 0.5*t+cshort+Dshort = a5 = a3*t*0.5*a3/(a3*t+a4*t) = a6 = 0.5*a3-a5 = a7 = a4*t*0.5*a4/(a3*t+a4*t) = a8 = 0.5*a4-a7 = a9 = Dlong+clong+1.414*t = a10 = Dshort+cshort+1.414*t = a11 = Dlong+clong+a10 = a12 = Dshort+cshort+a9 =
Two-way shear: 411.13.2.1
Shear capacity fv*Vc and maximum shear stress fv*vc: bo = a3+a4 = Vc1 = (1/6)*[1+2/(clong/cshort)]*sqrt(f'c/1,000,000)*bo*t*1,000,000 =
Vc2 = (1/12)*(as*t/b0+2)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = For corner column as = 20: Vc3 = (1/3)*sqrt(f'c/1,000,000)*bo*t*1,000,000 = Vc = smallest of Vc1, Vc2 or Vc3 = Shear capacity, fv*Vc = Maximum shear stress, fv*vc = fv*Vc/(bo*t) = Direct shear due to slab and wall loads, Vudirect: Vuslab = wtotal*[(a1*a2-a3*a4] = Vuwall = LFDL*Wwall*(a1+a2-a3-a4) = Vudirect = Vuslab+Vuwall = Vudirect/(fv*Vc) = Direct shear stress due to slab and wall loads, vudirect: vudirectb = vudirectc = vudirectd = Vudirect/(bo*t) = Moment about axis Z-Z to be transferred to the column (from column line A): 413.7.3.6
The gravity load moment to be transferred between slab and edge column shall be 0.3 MZZ = 0.30*MoA =
413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be tra gfZZ = 1/[1+(2/3)*sqrt(a4/a3)]
413.6.3.2
Capacity/Demand Ratio for flexure, moment about axis Z-Z: Moment be transferred by flexure MZZf = gfZZ*Mzz = Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort clong+3*t = clong+1.5*t+Dlong = Moment capacity Mcap = beff*MCSshort = Capacity/Demand Ratio = Mcap/MZZb = Slab adequate in bending if C/D > 1.0 Shear stress due to moment about axis Z-Z transferred by shear: Moment to be transferred by shear MZZv = (1-gfZZ)*Mzz = vuZZc = vuZZd = MZZv*a7/JZZ = vuZZb = -MZZv*(a4-a7)/JZZ = JZZ = Jbd+Jcd = Jbd = Ixbd+Iybd = Ixbd = a4*t3/12 = 3 2 Iybd = a4 *t/12+a4*t*a8 = 2 Jcd = (a3*t)*a7 = Moment about axis W-W to be transferred to the column (from column line 1):
413.7.3.6
The gravity load moment to be transferred between slab and edge column shall be 0.3 MWW = 0.30*Mo1 =
413.6.3.2
The fraction of the unbalanced moment given by g f *M u shall be considered to be tra gfWW = 1/[1+(2/3)*sqrt(a3/a4)] Capacity/Demand Ratio for flexure, moment about axis W-W: Moment be transferred by flexure MWWb = gfWW*MWW = Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort cshort+3*t = cshort+1.5*t+Dshort = Moment capacity Mcap = beff*MCSlong = Capacity/Demand Ratio = Mcap/MWWb = Slab adequate in bending if C/D > 1.0
Shear stress due to moment about axis W-W transferred by shear: Moment to be transferred by shear MWWv = (1-gfWW)*MWW = vuWWb = vuWWd = MWWv*a5/JWW = vuWWc = -MWWv*(a3-a5)/JWW = JWW = Jbd+Jcd = Jbd = (a4*t)*a52 = Jcd = Ixcd+Iycd = 3 Ixcd = a3*t /12 = 3 2 Iycd = a3 *t/12+(a3*t)*a6 = Shear stresses: vub = vudirectb+vuZZb+vuWWb = vuc = vudirectc+vuZZc+vuWWc = vud = vudirectd+vuZZd+vuWWd = Design shear stress: vu = largest of absolute values of vub, vuc or vud = Capacity/Demand Ratio for two-way shear: C/D Ratio for two-way shear = fv*vc/vu = Slab adequate in shear if C/D ratio > 1.0
One-way shear: 411.4.1.1
Shear capacity: bo = sqrt(a112+a122) = fv*Vc = fv*0.17*sqrt(f'c)*bo*t = Direct shear due to slab and wall load: Vuslab = wtotal*(a1*a2-0.5*a11*a12) = Vuwall = LFDL*Wwall*(a1+a2-a11-a12) = Vu = Vuslab+Vuwall = Capacity/Demand Ratio for one-way shear: C/D Ratio for one-way shear = fv*Vc/Vu = Slab adequate in shear if C/D ratio > 1.0
Page 6 of 6
a11 = Dlong+clong+a10 a12 = Dshort+cshort+a9
Long Direction Dshort
a9 = Dlong+clong+1.414*t
000)*bo*t*1,000,000 =
a2 = 0.44*Lshort+0.5*cshort+Dshort
45o
0.44*Lshort
t
a10 = Dshort+cshort+1.414*t
0.5*cshort
One-way shear
3.393 3.393 0.540 0.540 0.135 0.135 0.135 0.135 0.705 0.705 1.155 1.155
1.08 348,567.39
*bo*t*1,000,000 =
309,837.68 309,837.68 232,378.26 232,378.26 197,521.52 1,016,057.19 226,158.46 62,309.52 288,467.98 1.46 1,483,888.76
the column (from column line A):
etween slab and edge column shall be 0.3*M o . 131,721.71
n by g f *M u shall be considered to be transferred by flexure 60.00% about axis Z-Z: cshort+3*t or cshort+1.5*t+Dshort
79,033.03 0.720 0.990 0.720 0.00 Not adequate
ransferred by shear: 52,688.68 1,153,329.06 -3,459,987.17 0.00617 0.00440 0.00026 0.00413 0.00177
o the column (from column line 1):
etween slab and edge column shall be 0.3*M o . 131,722
n by g f *M u shall be considered to be transferred by flexure 60.00% about axis W-W: cshort+3*t or cshort+1.5*t+Dshort
79,033.03 0.720 0.990 0.720 0.00 Not adequate
W transferred by shear: 52,688.68 1,153,329.06 -3,459,987.17 0.00617 0.00177 0.00440 0.00026 0.00413 -822,769.35 -822,769.35 3,790,546.88 3,790,546.88 0.27 Not adequate
1.633 152,292.07 218,603.11 34,920.29 253,523.40 0.601 Not adequate
-822769.3
0.50*Lshort
Critical section
0.56*Lshort
0.56*Llong-0.5*clong-dave
clong+dave Critical Section 0.56*Llong
0.50*Lshort
cshort+dave 0.50*Llong
0.56*Lshort
Llong
Llong
