DESIGN OF SLAB
Caption Calculation Symbol =ValueUnitReference OR Explanation
Design Parameters
Partial Safety Factor for LoadsLimit State of Collapse (DL+LL)gf=1.5ConstantCl.36.4.1 of IS 456-2000
Partial Safety Factor for Steelgs=1.15ConstantCl.36.4.1 of IS 456-2000
Partial Safety Factor for Concretegc=1.5ConstantCl.36.4.1 of IS 456-2000
Elasticity of SteelEs=200000N/mm^2Cl 5.6.3 of IS 456-2000
Elasticity of ConcreteEc=19364.9167310371N/mm^2Cl 6.2.3.1 of IS 456-2000
Characteristic strength Concretefck=15N/mm^2
Characteristic strength Steelfy=415N/mm^2
Concrete Weightwc=25 kN/Cum
Member Sizes
Minimumn Bar DiaMin Dia=8mmSpecs
Max SpacingMax Spacing=450mmSpecs
Main Bar Dia proposedBar Dia=8mmUser specified
Clear CoverCover=15mmSpecs
Short Span LengthLx=3mDrawing
Long Span LengthLy=4mDrawing
Depth Management
Estimated effective depth=3000/32D(estd)=93.75mmFor Two Way - Contineous: Lx/32
Gross depth of slab=Round((93.75+8/ 2 + 15) / 10, 0) * 10Dg=110mmRound((D + mainBarDia / 2 + coverMain) / 10, 0) * 10
Effective depth= 110-8/ 2 -15D=93.75mmD = Dg - mainBarDia / 2 - coverMain
Loads
Self weight of slab=110*/1000*25SW=2.75kN-m^2
Live load on slabLL=3kN-m^2From IS-875
Floor finishes on slabFF=2.5kN-m^2User Defined
WL loads=2.75+3+2.5WL=8.25kN-m^2
Slab End Conditions
Left, Right, Top and Bottom=Left: S1 ; Right: S3; Top: S6; Bottom:S9
Moment Coeficients For Corners Held Down
Mid span Moment along the Long Span=(24 + (2 * 0) + (1.5 * (0) ^ 2)) / 1000aY=0.024Constant(24 + (2 * Nd) + (1.5 * (Nd) ^ 2)) / 1000
Moment coeft on SHORT Left EDGE=0.024* 4 / 3aY1=0.032ConstantEnd span Moment coeft along the Long Span: AlphaY * 4 / 3
Moment coeft on SHORT Right EDGE=0.024* 4 / 3aY2=0.032ConstantEnd span Moment coeft along the Long Span: AlphaY * 4 / 3
Moment Constant=(2 / 9) * (3 - (Sqr(18) * (3/4) * ((Sqr(0.024+0.032) + (Sqr(0.024+0.032))))))R=0.332Constant(2 / 9) * (3 - (Sqr(18) * (Lx / Ly) * ((Sqr(AlphaY + AlphaY1) + (Sqr(AlphaY + AlphaY2))))))
Long Edge Constant Top = 4 / 3K3=1.333ConstantIf Long Top Edge Continuous thenK3 = 4 / 3
Long Edge Constant Bottom= 4 / 3K4=1.333ConstantIf Long Bottom Edge Continuous thenK4 = 4 / 3
Mid span Moment along the Short Span=0.332/ (Sqr(1 +1.333) + Sqr(1 +1.333)) ^ 2aX=0.036ConstantR / (Sqr(1 + K3) + Sqr(1 + K4)) ^ 2
Moment coeft on LONG Top EDGE=0.036* 4 / 3aX1=0.048ConstantEnd span Moment coeft along the Short Span: AlphaX * 4 / 3
Moment coeft on LONG Bottom EDGE=0.036* 4 / 3aX2=0.048ConstantEnd span Moment coeft along the Short Span: AlphaX * 4 / 3
Slab Plan=
Moments
Mid span factored moment along Short span=1.5*0.036*8.25*3^ 2Mx=4.01kN-maX * WL * Lx ^ 2
Mid span factored moment along Long span=1.5*0.024*8.25*3^ 2My=2.67kN-maY * WL * Lx ^ 2
End span factored moment along Short span=1.5*0.048*8.25*3^ 2Mx1=5.35kN-maX1 * WL * Lx ^ 2
End span factored moment along Short span=1.5*0.048*8.25*3^ 2Mx2=5.35kN-maX2 * WL * Lx ^ 2
End span factored moment along Long span=1.5*0.032*8.25*3^ 2My1=3.56kN-maY1 * WL * Lx ^ 2
End span factored moment along Long span=1.5*0.032*8.25*3^ 2My2=3.56kN-maY2 * WL * Lx ^ 2
Self weight of slabLL=3kN-m^2From IS-875
Stress block Parameters for the estimated eff depth
Minimum Steel % Required= Max((0.12*1000*93.75/ 100),(1000/ 450* Atn(1) *8^ 2))ptMin=0.12%Max (Value * B * D / 100), (B / maxSpacing * PI/4 * MinDia ^ 2); IS 456 cl 26.5.2.1 min As = 0.12*b*d/100 for deformed bars
MR Produced by Min Steel %= 1000*(93.75^2) * ((415/1.15 ) * (0.12/100 ) * (1-(0.416 * (415/1.15) / (0.36*15) * (0.12/100))))/10^6Min-MR=3.679kN-mB * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Min Bar Dia #8Min Dia=8mmMinimum bar dia
Max Bar Spacing #8@450Spacing=450mmMaximum Spacing of bars
NO need to calculate MRs < this Min-MR
Ultimate strain in steel=(415/1.15/200000/)+0.002esu=0.0038Constant((fy / gs / Es) + 0.002
Limiting depth of neutral axis=(0.0035 / (0.0035 +0.0038)) *93.75Xu=44.922mm(0.0035 / (0.0035 + esu)) * D OR 0.48D
Parabolic depth from origin/neutral axis=0.002*44.922/ 0.0035X1=25.67mm0.002 * Xu / 0.0035
Total area constant of the stress block=(((2/3/1.5)*15*44.922*1000)-((2/3/1.5)*15*25.67/3*1000))/15/44.922/1000k1=0.36Constant0.364 * fck * x * b ; this can be taken as 0.36 for all practical purposes -cl 37.1 of IS 456-2000 {(((2 / 3 / gc) * fck * X * B) - ((2 / 3 / gc) * fck * X1 / 3 * B))}
Distance of the centre of compression from the compression edge=(44.922 - (((2/3/1.5) * 15*44.922*1000*(44.922/2) - ((2/3/1.5) *15*1000*25.67^ 2 /12))/(0.36*15*44.922*1000))) /44.922k2=0.416Constant0.416 OR say 0.42 as per IS 456 clause 37.1c ((X - (((2 / 3 / gc) * fck * X * B * (X / 2) - ((2 / 3 / gc) * fck * B * X1 ^ 2 / 12)) / (k1 * fck * X * B))) / X)
Moment of Resistance by Concrete Section=0.36*15*44.922*1000*(93.75-(0.416*44.922))MRc=18208521N-mm k1 * fck * xu * B * (D - (k2 * xu))
Coefficient of Moment of Resistance =18208520.508/(15*1000*8789.0625)k=0.138Constant0.138 for fe 415 (= Mu/ fck * B * D^2)
Minimum Depth of Section Required=Sqrt(5346000/ (0.138*15*1000))Dr=50.819mmUsing formula Mu = k * fck * B * D^2
DEPTH PROVIDED IS ADEQUATE
Steel>> mid span: Mx
Reqd Steel Percentage %=0.14pt=0.14%By trials; pt = 0.12 produces lower Moment of Resistance than 4.01
Moment of Resistance= 1000*(93.75^2) * ((415/1.15 ) * (0.14/100 ) * (1-(0.416 * (415/1.15) / (0.36*15) * (0.14/100))))/10^6MR=4.27kN-mB * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Required=0.14*1000*93.75/100Ast=131.25mm^2Ast = pt * B * D / 100
Bar SapcingProvide #8@380Spacing=380mm
Steel>> end span: Mx1
Reqd Steel Percentage %=0.18pt=0.18%By trials; pt = 0.16 produces lower Moment of Resistance than 5.346
Moment of Resistance= 1000*(93.75^2) * ((415/1.15 ) * (0.18/100 ) * (1-(0.416 * (415/1.15) / (0.36*15) * (0.18/100))))/10^6MR=5.42kN-mB * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Required=0.18*1000*93.75/100Ast=168.75mm^2Ast = pt * B * D / 100
Bar SapcingProvide #8@300Spacing=300mm
Stee>> end span: Mx2
Reqd Steel Percentage %=0.18pt=0.18%By trials; pt = 0.16 produces lower Moment of Resistance than 5.346
Moment of Resistance= 1000*(93.75^2) * ((415/1.15 ) * (0.18/100 ) * (1-(0.416 * (415/1.15) / (0.36*15) * (0.18/100))))/10^6MR=5.42kN-mB * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100))))
Steel Required=0.18*1000*93.75/100Ast=168.75mm^2Ast = pt * B * D / 100
Bar SapcingProvide #8@300Spacing=300mm