DESIGN OF SLAB
 Caption Calculation Symbol = Value Unit Reference OR Explanation Design Parameters Partial Safety Factor for Loads Limit State of Collapse (DL+LL) gf = 1.5 Constant Cl.36.4.1 of IS 456-2000 Partial Safety Factor for Steel gs = 1.15 Constant Cl.36.4.1 of IS 456-2000 Partial Safety Factor for Concrete gc = 1.5 Constant Cl.36.4.1 of IS 456-2000 Elasticity of Steel Es = 200000 N/mm^2 Cl 5.6.3 of IS 456-2000 Elasticity of Concrete Ec = 19364.9167310371 N/mm^2 Cl 6.2.3.1 of IS 456-2000 Characteristic strength Concrete fck = 15 N/mm^2 Characteristic strength Steel fy = 415 N/mm^2 Concrete Weight wc = 25 kN/Cum Member Sizes Minimumn Bar Dia Min Dia = 8 mm Specs Max Spacing Max Spacing = 450 mm Specs Main Bar Dia proposed Bar Dia = 8 mm User specified Clear Cover Cover = 15 mm Specs Short Span Length Lx = 3 m Drawing Long Span Length Ly = 4 m Drawing Depth Management Estimated effective depth =3000/32 D(estd) = 93.75 mm For Two Way - Contineous: Lx/32 Gross depth of slab =Round((93.75+8/ 2 + 15) / 10, 0) * 10 Dg = 110 mm Round((D + mainBarDia / 2 + coverMain) / 10, 0) * 10 Effective depth = 110-8/ 2 -15 D = 93.75 mm D = Dg - mainBarDia / 2 - coverMain Loads Self weight of slab =110*/1000*25 SW = 2.75 kN-m^2 Live load on slab LL = 3 kN-m^2 From IS-875 Floor finishes on slab FF = 2.5 kN-m^2 User Defined WL loads =2.75+3+2.5 WL = 8.25 kN-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)) / 1000 aY = 0.024 Constant (24 + (2 * Nd) + (1.5 * (Nd) ^ 2)) / 1000 Moment coeft on SHORT Left EDGE =0.024* 4 / 3 aY1 = 0.032 Constant End span Moment coeft along the Long Span: AlphaY * 4 / 3 Moment coeft on SHORT Right EDGE =0.024* 4 / 3 aY2 = 0.032 Constant End 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 = 0.332 Constant (2 / 9) * (3 - (Sqr(18) * (Lx / Ly) * ((Sqr(AlphaY + AlphaY1) + (Sqr(AlphaY + AlphaY2)))))) Long Edge Constant Top = 4 / 3 K3 = 1.333 Constant If Long Top Edge Continuous thenK3 = 4 / 3 Long Edge Constant Bottom = 4 / 3 K4 = 1.333 Constant If Long Bottom Edge Continuous thenK4 = 4 / 3 Mid span Moment along the Short Span =0.332/ (Sqr(1 +1.333) + Sqr(1 +1.333)) ^ 2 aX = 0.036 Constant R / (Sqr(1 + K3) + Sqr(1 + K4)) ^ 2 Moment coeft on LONG Top EDGE =0.036* 4 / 3 aX1 = 0.048 Constant End span Moment coeft along the Short Span: AlphaX * 4 / 3 Moment coeft on LONG Bottom EDGE =0.036* 4 / 3 aX2 = 0.048 Constant End 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^ 2 Mx = 4.01 kN-m aX * WL * Lx ^ 2 Mid span factored moment along Long span =1.5*0.024*8.25*3^ 2 My = 2.67 kN-m aY * WL * Lx ^ 2 End span factored moment along Short span =1.5*0.048*8.25*3^ 2 Mx1 = 5.35 kN-m aX1 * WL * Lx ^ 2 End span factored moment along Short span =1.5*0.048*8.25*3^ 2 Mx2 = 5.35 kN-m aX2 * WL * Lx ^ 2 End span factored moment along Long span =1.5*0.032*8.25*3^ 2 My1 = 3.56 kN-m aY1 * WL * Lx ^ 2 End span factored moment along Long span =1.5*0.032*8.25*3^ 2 My2 = 3.56 kN-m aY2 * WL * Lx ^ 2 Self weight of slab LL = 3 kN-m^2 From 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))))/10^6 Min-MR = 3.679 kN-m B * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100)))) Min Bar Dia #8 Min Dia = 8 mm Minimum bar dia Max Bar Spacing #8@450 Spacing = 450 mm Maximum Spacing of bars NO need to calculate MRs < this Min-MR Ultimate strain in steel =(415/1.15/200000/)+0.002 esu = 0.0038 Constant ((fy / gs / Es) + 0.002 Limiting depth of neutral axis =(0.0035 / (0.0035 +0.0038)) *93.75 Xu = 44.922 mm (0.0035 / (0.0035 + esu)) * D OR 0.48D Parabolic depth from origin/neutral axis =0.002*44.922/ 0.0035 X1 = 25.67 mm 0.002 * 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))/15/44.922/1000 k1 = 0.36 Constant 0.364 * 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))) /44.922 k2 = 0.416 Constant 0.416 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 = 18208521 N-mm k1 * fck * xu * B * (D - (k2 * xu)) Coefficient of Moment of Resistance =18208520.508/(15*1000*8789.0625) k = 0.138 Constant 0.138 for fe 415 (= Mu/ fck * B * D^2) Minimum Depth of Section Required =Sqrt(5346000/ (0.138*15*1000)) Dr = 50.819 mm Using formula Mu = k * fck * B * D^2 DEPTH PROVIDED IS ADEQUATE Steel>> mid span: Mx Reqd Steel Percentage % =0.14 pt = 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))))/10^6 MR = 4.27 kN-m B * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100)))) Steel Required =0.14*1000*93.75/100 Ast = 131.25 mm^2 Ast = pt * B * D / 100 Bar Sapcing Provide #8@380 Spacing = 380 mm Steel>> end span: Mx1 Reqd Steel Percentage % =0.18 pt = 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))))/10^6 MR = 5.42 kN-m B * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100)))) Steel Required =0.18*1000*93.75/100 Ast = 168.75 mm^2 Ast = pt * B * D / 100 Bar Sapcing Provide #8@300 Spacing = 300 mm Stee>> end span: Mx2 Reqd Steel Percentage % =0.18 pt = 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))))/10^6 MR = 5.42 kN-m B * (D ^ 2) * ((fy / gs) * (pt / 100) * (1 - (k2 * (fy / gs) / (k1 * fck) * (pt / 100)))) Steel Required =0.18*1000*93.75/100 Ast = 168.75 mm^2 Ast = pt * B * D / 100 Bar Sapcing Provide #8@300 Spacing = 300 mm