Flat Slab

SLAB DESIGN WORKSHEETTwo-Way Post-Tensioned Flat Plate (slab without beams)Project:Designer:Date:

All units are in Newtons and meters unless otherwise indicated

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).

5. Slab is of uniform thickness.6. Direct design method is applicable.

Fixed inputs:

3. There may or may not be any overhang (Dlong and/or Dshort may or may not be zero)

4. There may or may not be any wall load (Wwall may or may not be zero).

Span in long direction, Llong =

Llong

CornerSlab

EdgeSlab 1

L sho

rtL s

hort

Dlong

Dsh

ort

Shor

tD

irecti

on

A

1

2

3

Floor to floor height, H =

426.409.3.2.1

426.409.3.2.3

Superimposed dead load:

426.409.2.1

Design inputs:Slab thickness, t =

204-1

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 =

Column width in short direction, cshort =

Capacity reduction factor for flexure fb =

Capacity reduction factor for shear fv =

Live load, wLL =

Floor finish, waterproofing, etc., wDL1 =

Other dead loads, wDL2 =

Exterior wall load, Wwall (N/m) =

Load Factor for Dead Load, LFDL =

Load Factor for Live Load, LFLL =

Unit weight of concrete gconc =

Concrete strength, f'c =

Steel yield strength, fy =

m= fy/0.85*f'c =

of 6


1. All spans (long and short direction) are uniform length.2. All columns have uniform dimensions (long and short direction).

7.200

long and/or Dshort may or may not be zero)

wall may or may not be zero).

Llong

EdgeSlab 2

InteriorSlab

LongDirection

cshort

clong

B C

6.750

0.000

7.200

6.750

0.000

0.450

0.4504.500

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

nlong = Llong-clong =

nshort = Lshort-cshort =


409.6.3.2 Minimum slab thickness:

Table 409-3 Minimum slab thicknessYield Strength Exterior Panels Interior Panels280,000,000 0.205 0.188309,000,000 0.209 0.191415,000,000 0.225 0.205

N.A. 0.000 0.000520,000,000 0.241 0.218

Uniform load on slab:Dead Load:

Live Load =

Direct design method criteria:413.7.1.1 1. There are a minimum of three continous spans in each direction.413.7.1.2 2. Panels are rectangular, with ratio of longer to shorter span center-to-center support within a

panel not greater than 2.413.7.1.3 3. Successive span lengths center-to-center supports in each direction do not differ by more than

one-third the longer span.413.7.1.4 4. Offsets of columns are a minimum of 10% of the span in direction of offset from either axis

between center lines of successive columns.413.7.1.5 5. All loads shall be due to gravity loads only and distributed over the entire panel.413.7.1.5 6. Live load shall not exceed two times the dead load.413.7.1.6 7. The relative stiffness of beams in two perpendicular directions

shall not be less than 0.2 nor greater than 5.0.

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 =

Slab weight, wDLslab = t*gconc =

Floor finish, waterproofing, etc., wDL1 =

Other dead loads, wDL2 =

wDL = wDLslab+wDLothers =

Total load, wtotal = LFLL*wLL+LFDL*wDL =

(af1*L22)/af2*L1

2)

of 6

0.209

0.191

0.191

0.94

4,248

3,120

1,200

8,5684,800

20,155

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 a

3. Successive span lengths center-to-center supports in each direction do not differ by more than

4. Offsets of columns are a minimum of 10% of the span in direction of offset from either axis

5. All loads shall be due to gravity loads only and distributed over the entire panel.

7. The relative stiffness of beams in two perpendicular directions



Moment analysis:Slab strips in long direction:

Slab strips in short direction:

Column strip

Half middle strip

Column strip

3

2

1

Hal

f mid

dle

strip

Colu

mn

strip

Colu

mn

strip

3

2

1

A B

A B

Half middle strip

Half middle strip

Shor

tD

irecti

on

Hal

f mid

dle

strip

Hal

f mid

dle

strip

Colu

mn

strip

Colu

mn

strip

3

Shor

tD

irecti

on

Hal

f mid

dle

strip

of 6


Column strip

Half middle strip

Column strip

C

C

0.50*Lshort+0.5*cshort+Dshort

Half middle strip

Half middle strip

L sho

rt

LongDirection

Hal

f mid

dle

strip

Dsh

ort

0.5*

L sho

rt0.5*cshort

Hal

f mid

dle

strip


413.7.2.2 Total factored static moment:Slab strips in long direction:

Slab strips in short direction:

Wall load:

413.7.3.3 Calculation of longitudinal moments

Frame 1

439,072

-M at exterior support 114,159+M at exterior span 0.52*Mo 228,318-M at first interior support 0.70*Mo 307,351-M at typical interior support 0.65*Mo 285,397+M at typical interior support 0.35*Mo 153,675

413.7.4.2 Percentage of exterior negative moment going to column strip:

Frames 1 and 2:

0.500 1.000 1.000

0 100.00% 100.00%0.09 99.07% 99.07% 99.07%

2.5 75.00% 75.00% 75.00%

Column strip %, exterior negative moment

Frames 1 & 2 1.000 0.000 0.000Frames A & B 1.000 0.000 0.000

Torsional constant C:In long direction:

In short direction:

Slab strip 1: Mo1 = wtotal*(0.5*Lshort+0.5*cshort+Dshort)*Lnlong2/8 =

Slab strip 2: Mo2 = wtotal*Lshort*Lnlong2/8 =

Slab strip A: MoA = wtotal*(0.5*Llong+0.5*clong*Dlong)*Lnshort2/8 =

Slab strip B: MoB = wtotal*Llong*Lnshort2/8 =

In long direction: Mow1 = LFDL*Wwall*Lnlong2/8 =

In short direction: MowA = LFDL*Wwall*Lnshort2/8 =

Mo1

Mo

0.26*Mo

L2/L1

bt =

bt >

L2/L1 a1 a1*(L2/L1)

Clong = (1-0.63*t/cshort)*(t3*cshort/3) =

Cshort = (1-0.63*t/clong)*(t3*clong/3) =

cshort t

cclong 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:

Totalmoment

Frame 1 Exterior span -Mext 114,159+M 228,318

-Mint 307,351Interior span -M 285,397

+M 153,675Frame 2 Exterior span -Mext 214,887

+M 429,774-Mint 578,542

Interior span -M 537,218+M 289,271

Frame A Exterior span -Mext 114,159+M 228,318

-Mint 307,351Interior span -M 285,397

+M 153,675Frame B Exterior span -Mext 214,887

+M 429,774-Mint 578,542

Interior span -M 537,218+M 289,271

439,072.37

826,489.17

439,072.37

826,489.17

62,192.81

62,192.81

Frame 2 Frame A Frame B Wall 1 Wall A

826,489 439,072 826,489 62,193 62,193

214,887 114,159 214,887 16,170 16,170429,774 228,318 429,774 32,340 32,340578,542 307,351 578,542 43,535 43,535537,218 285,397 537,218 40,425 40,425289,271 153,675 289,271 21,767 21,767

Frames A and B:

1.000 1.000 2.000

0 100.00% 100.00%0.09 99.07% 99.07% 99.07%

2.5 75.00% 75.00% 75.00%

Column strip %, exterior negative moment

C %0.00065 0.00350 0.094 99.07%0.00065 0.00350 0.094 99.07%

0.000654

0.000654

short+Dshort)*Lnlong2/8 =

*Dlong)*Lnshort2/8 =

Mo2 MoA MoB MoW1 MoWA

L2/L1

bt =

bt >

Is bt

= (1-0.63*t/cshort)*(t3*cshort/3) =

= (1-0.63*t/clong)*(t3*clong/3) =

Percentage of interior negative moments going to column strip = 75.00%

60.00%

% momnt Moment in Moment Momentto column column strip in column in middlestrip slab slab wall strip slab strip slab99.07% 113,091 16,170 129,262 1,06760.00% 136,991 32,340 169,331 91,32775.00% 230,513 43,535 274,048 76,83875.00% 214,048 40,425 254,473 71,34960.00% 92,205 21,767 113,973 61,47099.07% 212,878 212,878 2,00960.00% 257,865 257,865 171,91075.00% 433,907 433,907 144,63675.00% 402,913 402,913 134,30460.00% 173,563 173,563 115,70899.07% 113,091 16,170 129,262 1,06760.00% 136,991 32,340 169,331 91,32775.00% 230,513 43,535 274,048 76,83875.00% 214,048 40,425 254,473 71,34960.00% 92,205 21,767 113,973 61,47099.07% 212,878 212,878 2,00960.00% 257,865 257,865 171,91075.00% 433,907 433,907 144,63675.00% 402,913 402,913 134,30460.00% 173,563 173,563 115,708


Shear analysis:Edge column B1:

411.13.2.1

a1 = 1.06*Llong =a2 = Dshort+0.5*cshort+0.44*Lshort =a3 = clong+t =a4 = Dshort+cshort+0.5*t =a5 = (Aac*0.5*a4+Abd*0.5*a4)/(Acd+Aac+Abd) =

Aac = Abd = a4*t =Acd = a3*t =

a6 = 0.5*a4-a5 =

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 = 30Vc3 = (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) =

C

0.56*Llong

a1 = 1.06*Llong

Z

W

W

a3 = clong+t

Centroid ofshear perimeter

a

c

Shor

t dire

ction

B

1

Moment about axis Z-Z to be transferred to the column:413.7.3.6

413.6.3.2

413.6.3.3

Capacity/Demand Ratio for flexure, moment about axis Z-Z:

413.6.3.2

Slab adequate in bending if C/D > 1.0Shear stress due to moment about axis Z-Z transferred by shear:

Moment about axis W-W to be transferred to the column (from column line 1 with LL on span A-B only):

413.6.3.2

413.6.3.3

Capacity/Demand Ratio for flexure, moment about axis W-W:

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) =

The gravity load moment to be transferred between slab and edge column shall be 0.3*Mo.MZZ = 0.30*MoB =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfZZ1 = 1/[1+(2/3)*sqrt(a4/a3)]For edge columns with unbalanced moments about an axis parallel to the edge, gf = 1.0 provided thatVu at an edge support does not exceed 0.75*fv*Vc

gfZZ = gfaZZ1 if Vudirect/(fv*Vc)>0.75; gfZZ = 100% if Vudirect/(fv*Vc)<0.75

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 =

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 = a4

3*t/12+(a4*t)*a62 =

Jcd = (a3*t)*a52 =

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*wDL/wtotal)*M2 =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 =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfaWW = 1/[1+(2/3)*sqrt(a3/a4)]For edge columns with unbalanced moments about an axis transverse to the edge, increase gf to as much as1.25 times the value but not more than 1.0 provided that Vu at the support does not exceed 0.40*fv*Vc.Percentage of moment transferred by flexure, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40

Moment be transferred by flexure MWWb = gfWW*MWW =

Slab adequate in bending if C/D > 1.0Shear stress due to moment about axis W-W transferred by shear:

Shear stresses:

Critical shear stress:

Capacity/Demand Ratio for shear:

Slab adequate in shear if C/D ratio > 1.0

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 =

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 =

Ixcd = a3*t3/12 =Iycd = a3

3*t/12 =Jac = Jbd = a4*t*(0.5*a3)2 =

vua = vudirecta+vuZZa+vuWWa =vub = vudirectb+vuZZv+vuWWb =vuc = vudirectc+vuZZc+vuWWc =vud = vudirectd+vuZZd+vuWWd =

vu = largest of absolute values of vua, vub, vuc or vud =

C/D Ratio = fv*vc/vu =

of 6

7.6323.3930.6300.5400.1710.0970.1130.099

1.71551,898.36474,438.94

367,932.24367,932.24312,742.40

1,016,057.19

/1,000,000)*bo*t*1,000,000 =/1,000,000)*bo*t*1,000,000 =

0.50*Llong

a1 = 1.06*Llong

Dsh

ort

0.5*cshort

0.44

*Lsh

ort

a 2 =

0.4

4*L s

hort+0

.5*c

shor

t+D

shor

t

Z

W

W

a3 = clong+t

a 4 =

0.5

*t+c

shor

t+D

shor

t

0.5*

a 4

a 5a 6

b

d

Long direction

B

515,069.6876,461.84

591,531.521.89

1,921,804.82Moment about axis Z-Z to be transferred to the column:

247,946.75

61.83%

61.83%Capacity/Demand Ratio for flexure, moment about axis Z-Z:

153,317.270.99

0.00Not adequate

Shear stress due to moment about axis Z-Z transferred by shear:94,629.48

1,541,246.89-3,339,368.25

0.010470.003590.000260.003320.00330


307,351285,397169,852137,499

43,53540,425

3,110140,609

58.14%

58.14%Capacity/Demand Ratio for flexure, moment about axis W-W:

81,745.29

Direct shear stress due to slab and wall loads, vudirect:

The gravity load moment to be transferred between slab and edge column shall be 0.3*Mo.

The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexure

For edge columns with unbalanced moments about an axis parallel to the edge, gf = 1.0 provided that

= 100% if Vudirect/(fv*Vc)<0.75

= (1-gfZZ)*Mzz =

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*wDL/wtotal)*M2 =

Negative moment at first interior support M1 = 0.70*Mow1 =Negative moment at typical interior support M2 = 0.65*Mow1 =


For edge columns with unbalanced moments about an axis transverse to the edge, increase gf to as much as1.25 times the value but not more than 1.0 provided that Vu at the support does not exceed 0.40*fv*Vc.Percentage of moment transferred by flexure, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40

fWW*MWW =

0.7200.9900.720

0.00Not adequate

Shear stress due to moment about axis W-W transferred by shear:58,863.33

794,216.20-794,216.20

0.023350.004060.000310.003750.00964

-623,347.23-2,211,779.644,257,267.912,668,835.50

4,257,267.91

0.24Not adequate

= shorter of cshort+3*t or cshort+1.5*t+Dshort

= (1-gfWW)*MWW =

uc or vud =

474,438.94

-22117804257267.91

Criti

cal s

ectio

n

0.50

*Lsh

ort

Criti

cal s

ectio

n

0.56*Llong-0.5*clong-dave0.56

*Lsh

ort

0.50

*Lsh

ort

clong+dave0.50*Lshort

Llong

0.50*Llong0.56*Lshort

clong+dave

cshort+daveCriticalSection

0.50*Lshort

0.56*Llong


Edge column A2:

411.13.2.1

a1 = 1.06*Lshort =a2 = Dlong+0.5*clong+0.44*Llong =a3 = cshort+t =a4 = Dlong+clong+0.5*t =a5 = (Aac*0.5*a4+Abd*0.5*a4)/(Acd+Aac+Abd) =

Aac = Abd = a4*t =Acd = a3*t =

a6 = 0.5*a4-a5 =

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 =

Dlong 0.44*Llong

a2 = Dlong+0.5*clong+0.44*Llong

ZZ

W W

a4 = Dlong+clong+0.5*t

a 3 =

csh

ort+

t

Cent

roid

of

shea

r per

imet

er

Shor

t di

recti

onA

2

0.5*clong

0.5*a4

a6 a5

ab

cd

Moment about axis Z-Z to be transferred to the column:413.7.3.6

413.6.3.2

413.6.3.3


413.6.3.2


Moment about axis W-W to be transferred to the column (from column line A with LL on span 1-2 only):

413.6.3.2

For edge column, as = 30Vc3 = (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) =

The gravity load moment to be transferred between slab and edge column shall be 0.3*Mo.MZZ = 0.30*Mo2 =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfZZ1 = 1/[1+(2/3)*sqrt(a4/a3)]For edge columns with unbalanced moments about an axis parallel to the edge, gf = 1.0 provided thatVu at an edge support does not exceed 0.75*fv*Vc

gfZZ = gfaZZ1 if Vudirect/(fv*Vc)>0.75; gfZZ = 100% if Vudirect/(fv*Vc)<0.75

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 =

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 =


3*t/12+(a4*t)*a62 =

Jcd = (a3*t)*a52 =

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/wtotal)*M2 =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 =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfaWW = 1/[1+(2/3)*sqrt(a3/a4)]

413.6.3.3



Shear stresses:




For edge columns with unbalanced moments about an axis transverse to the edge, increase gf to as much as1.25 times the value but not more than 1.0 provided that Vu at the support does not exceed 0.40*fv*Vc.Percentage of moment transferred by flexure, gfWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40

Moment be transferred by flexure MWWb = gfWW*MWW =Effective width for flexure = beff = shorter of cshort+3*t or cshort+1.5*t+Dshort


Moment capacity Mcap = beff*MCSlong =C/D Ratio = Mcap/MWWb =

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 =


3*t/12 =Jac = Jbd = a4*t*(0.5*a3)2 =

vua = vudirecta+vuZZa+vuWWa =vub = vudirectb+vuZZb+vuWWb =vuc = vudirectc+vuZZc+vuWWc =vud = vudirectd+vuZZd+vuWWd =

vu = largest of vua, vub, vuc or vud =

C/D Ratio = fv*vc/vu =

/1,000,000)*bo*t*1,000,000 =*t*1,000,000 =

0.56

*Lsh

ort

0.50

*Lsh

ort

a 1 =

1.0

6*L s

hort

Long direction


Shear stress due to moment about axis Z-Z transferred by shear:

Moment about axis W-W to be transferred to the column (from column line A with LL on span 1-2 only):



For edge columns with unbalanced moments about an axis parallel to the edge, gf = 1.0 provided that

udirect/(fv*Vc)<0.75

Negative moment at first interior support M1 = 0.70*MoA =Negative moment at typical interior support M2 = 0.65*M0A =


Negative moment at first interior support M1 = 0.70*MowA =Negative moment at typical interior support M2 = 0.65*MowA =



Shear stress due to moment about axis W-W transferred by shear:

For edge columns with unbalanced moments about an axis transverse to the edge, increase gf to as much as1.25 times the value but not more than 1.0 provided that Vu at the support does not exceed 0.40*fv*Vc.

fWW = gfaWW if Vudirect/Vc>0.40; gf = 1.25*gfaWW if Vudirect/Vc<0.40

+3*t or cshort+1.5*t+Dshort

fWW)*MWW =

of 6

7.6323.3930.6300.5400.1710.0970.1130.099

1.71551,898.36474,438.94 474,438.94

30367,932.24367,932.24312,742.40

1,016,057.19

515,069.6876,461.84

591,531.521.89

1,921,804.82

247,946.75

61.83%

61.83%

153,317.270.99

0.00Not adequate

9,038,176.19147,206,361.56

-318,947,116.710.010470.003590.000260.003320.00330

307,351285,397169,852137,499

43,53540,425

3,110140,609

58.14%

58.14%

81,745.290.7200.9900.720

0.00Not adequate

58,863.33794,216.20

-794,216.200.023350.004060.000310.003750.00964

-317,819,528.09-316,231,095.69 -317819528148,333,950.18 -317819528149,922,382.58

-317,819,528.09

0.00Not adequate

0.56

*Lsh

ort

0.50

*Lsh

ort

Criti

cal s

ectio

n


*Lsh

ort

0.50

*Lsh

ort

Llong


clong+dave


0.50*Lshort

0.56*Llong


Interior column B2:

411.13.2.1

a1 = 1.06*Llong =a2 = 1.06*Lshort =a3 = clong+t =a4 = 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 = 40Vc3 = (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) =


0.56*Llong

a1 = 1.06*Llong

a3 = clong+t

W

W

Z Z

a b

c d

Shor

t dire

ction

B

2

Moment about axis Z-Z to be transferred to the column (from column line B with LL on span 1-2 only):

413.6.3.2


413.6.3.2



413.6.3.2Capacity/Demand Ratio for flexure, moment about axis W-W:


Shear stresses:

vudirecta = vudirectb = vudirectc = vudirectd = Vudirect/(bo*t) =

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 =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfZZ = 1/[1+(2/3)*sqrt(a4/a3)]

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 =

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 =


3*t/12 =Jab = Jcd = (a3*t)*(0.5*a4)2 =

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)*M2 =MWW = M1-M3 =gfWW = 1/[1+(2/3)*sqrt(a3/a4)]



Moment capacity Mcap = beff*MCSlong =Capacity/Demand Ratio = Mcap/MWWb =

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 =Iyab = a3

3*t/12 =

vua = vudirecta+vuZZa+vuWWa =




vub = vudirectb+vuZZb+vuWWb =vuc = vudirectc+vuZZc+vuWWc =vud = vudirectd+vuZZd+vuWWd =

vu = largest of absolute values of vua, vub, vuc or vud =

C/D Ratio for shear = fv*vc/vu =

of 6

7.6327.6320.6300.630

2.52813,323.90658,405.06

40542,215.93542,215.93460,883.54

1,016,057.19

1,165,988.882.53

/1,000,000)*bo*t*1,000,000 =*t*1,000,000 =

0.56

*Lsh

ort

0.50

*Lsh

ort

a 2 =

1.0

6*L s

hort

0.50*Llong

a 4 =

csh

ort+

t

Z

Long Direction

2,570,522.23Moment about axis Z-Z to be transferred to the column (from column line B with LL on span 1-2 only):

578,542.42537,217.96319,720.81338,751.81

60.00%Capacity/Demand Ratio for flexure, moment about axis Z-Z:

203,251.090.990

0.00Not adequate

Shear stress due to moment about axis Z-Z transferred by shear:135,500.72

1,394,040.37-1,394,040.37

0.030618000.004060.000310.003750.01125

Moment about axis W-W to be transferred to the column (from column line 2 with LL on span A-B only):578,542537,218319,721258,82260.00%

Capacity/Demand Ratio for flexure, moment about axis W-W:155,292.97

0.7200.9900.720

0.00Not adequate

Shear stress due to moment about axis W-W transferred by shear:103,528.64

1,065,109.50-1,065,109.50

0.030620.011250.004060.000310.00375

5,029,672.10

= 0.70*MoB = = 0.65*MoB =



= 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)*M2 =

+3*t or cshort+1.5*t+Dshort

fWW)*MWW =

2,899,453.102,241,591.35

111,372.35

5,029,672.10

0.20Not adequate

658,405.06

233805.4

5029672.15029672.1

Criti

cal s

ectio

n


*Lsh

ort

0.50

*Lsh

ort

Llong


clong+dave


0.50*Lshort

0.56*Llong


Corner column A1:

Two-way shear:

411.13.2.1

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 =

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 =

0.44*Llong

a1 = Dlong+0.5*clong+0.44*Llong


a4 = 0.5*t+cshort

+Dshort

W

W

Z

a b

c d

Shor

t dire

ction

A

1

Dlong 0.5*clong

a 7a 8

0.5*

a 4

Centroid ofshear perimeter

0.5*a3

a5a6

Z

Two-way shear

Moment about axis Z-Z to be transferred to the column (from column line A):413.7.3.6

413.6.3.2


413.6.3.2


Moment about axis W-W to be transferred to the column (from column line 1):413.7.3.6

413.6.3.2


Slab adequate in bending if C/D > 1.0

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) =

The gravity load moment to be transferred between slab and edge column shall be 0.3*Mo.MZZ = 0.30*MoA =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfZZ = 1/[1+(2/3)*sqrt(a4/a3)]

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 =

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 =Iybd = a4

3*t/12+a4*t*a82 =

Jcd = (a3*t)*a72 =

The gravity load moment to be transferred between slab and edge column shall be 0.3*Mo.MWW = 0.30*Mo1 =The fraction of the unbalanced moment given by gf*Mu shall be considered to be transferred by flexuregfWW = 1/[1+(2/3)*sqrt(a3/a4)]



Moment capacity Mcap = beff*MCSlong =Capacity/Demand Ratio = Mcap/MWWb =

Shear stress due to moment about axis W-W transferred by shear:

Shear stresses:

Design shear stress:

Capacity/Demand Ratio for two-way shear:

Slab adequate in shear if C/D ratio > 1.0One-way shear:

Shear capacity:

411.4.1.1Direct shear due to slab and wall load:

Capacity/Demand Ratio for one-way 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)*a5

2 =Jcd = Ixcd+Iycd =


3*t/12+(a3*t)*a62 =

vub = vudirectb+vuZZb+vuWWb =vuc = vudirectc+vuZZc+vuWWc =vud = vudirectd+vuZZd+vuWWd =

vu = largest of absolute values of vub, vuc or vud =

C/D Ratio for two-way shear = fv*vc/vu =

bo = sqrt(a112+a12

2) =fv*Vc = fv*0.17*sqrt(f'c)*bo*t =

Vuslab = wtotal*(a1*a2-0.5*a11*a12) =Vuwall = LFDL*Wwall*(a1+a2-a11-a12) =Vu = Vuslab+Vuwall =

C/D Ratio for one-way shear = fv*Vc/Vu =

and maximum shear stress fv*vc:

/1,000,000)*bo*t*1,000,000 =

0.5*cshort

t

a 10 =

Dsh

ort+

c sho

rt+1

.414

*t


a11 = Dlong+clong+a10

a 12 =

Dsh

ort+

c sho

rt+a

9

One-way shear

45o

Moment about axis Z-Z to be transferred to the column (from column line A):


Shear stress due to moment about axis Z-Z transferred by shear:

Moment about axis W-W to be transferred to the column (from column line 1):


/1,000,000)*bo*t*1,000,000 =




= shorter of cshort+3*t or cshort+1.5*t+Dshort

= (1-gfZZ)*Mzz =



fWW*MWW = = shorter of cshort+3*t or cshort+1.5*t+Dshort

Shear stress due to moment about axis W-W transferred by shear: = (1-gfWW)*MWW =

of 6

3.3933.3930.5400.5400.1350.1350.1350.1350.7050.7051.1551.155

1.08348,567.39

a 2 =

0.4

4*L s

hort+0

.5*c

s hor

t+D

shor

t

Long DirectionDshort

0.5*cshort

0.44

*Lsh

ort

309,837.68 309,837.68

232,378.26232,378.26197,521.52

1,016,057.19

226,158.4662,309.52

288,467.981.46

1,483,888.76

131,721.71

60.00%

79,033.030.7200.9900.720

0.00Not adequate

52,688.681,153,329.06

-3,459,987.170.006170.004400.000260.004130.00177

131,722

60.00%

79,033.030.7200.9900.720

0.00Not adequate

52,688.681,153,329.06

-3,459,987.170.006170.001770.004400.000260.00413

-822,769.35-822,769.35 -822769.35

3,790,546.88

3,790,546.88

0.27Not adequate

1.633152,292.07

218,603.1134,920.29

253,523.40

0.601Not adequate


*Lsh

ort

0.50

*Lsh

ort

Criti

cal s

ectio

n

0.56*Llong-0.5*clong-dave

Llong


clong+dave


0.50*Lshort

0.56*Llong

Flat Slab

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Transcript of Flat Slab