Two Way Slab Deflection 3b4d1b

DEFLECTION OF TWO WAY SLAB ** 1 2 3 4 5 6 7 8 9 10 11

Given Data :Longer Span c/c Shorter Span c/c Width of Slab considered breadth of web(bw) Live load Floor Finish Concrete Grade Steel Grade Thickness of slab Effective Cover to R/F = Area of steel provided (As per width considered) 12 Effective depth 13 Boundry Conditions Longer Edge1 = Longer Edge2 = Shorter Edge1= Shorter Edge2= No. of discontineous Edges Nd=

ly = lx = b= bw= wl = wff = fck = fy = D= d' = Ast= Asc= d= Cl1= Cl2= Cs1= Cs2=

14 Value of K3

K3=

15 Ultimate shrinkage strain of concrete (Ecs)= 16 Ultimate creep coefficient= ** Span Ratio ** Loading on Slab Self weight (D * 25) Live Load Floor finishes Total Service load

4500 4500 1000 1000 0.75 1 25 415 100 35 288 144 65 1.5275 1.5275 1.5275 1.5275 0

Continuous Continuous Continuous Continuous

0.063

1

2.5 0.75 1.00 4.25

kN/sq.m kN/sq.m kN/sq.m kN/sq.m

** Codal moment coefficients :Shorter Span Coeff (At midspan) **

Bending Moments :Along Shorter Direction (At midspan)

** Design Constant:-

0.0714309312

M(DL+LL) M(DL) M(LL)

6.15E+06 5.06E+06 1.08E+06

1 for Discontinuous edge 1.5275 for continuous edge

0.5 for cantilever 0.125 for simply ed 0.086 for continuous at on 0.063 for fully continuous end

0.0003 1.6

r =

S.W= L.L= F.F= W=

mm mm mm mm kN/sq.m kN/sq.m N/sqmm N/sqmm mm mm sqmm sqmm mm

Nmm Nmm Nmm

Modulus of Elasticity of Steel Modulus of Elasticity of Concrete

Es= Ec=

200000.00 N/sq.mm 25000.00 N/sq.mm

** Calculations:Modular ratio Gross Moment of Inertia Modulus of rupture of concrete Cracking Moment Neutral axis Lever arm Second Moment of area of cracked section Effective second moment of area

m= Igr= fcr= Mr= x= z= Icr= Ieff=

8.00 8.33E+07 3.50 5.83E+06 15.16 59.95 6.88E+06 1.30E+07

Alpha =

0.021

mm4 N/sq.mm Nmm mm mm mm4 mm4

** Short term deflection :-

y =(Alpha*w*lx*lx*lx*lx*B)/(Ec*12*Ieff) = Deflection due to DL+LL Deflection due to DL Deflection due to LL

y(DL+LL)= y(DL)= y(LL)=

Elastic Deflection (DL+LL) = Elastic Deflection (LL) =

9.372 mm 7.718 mm 1.654 mm

r= ly/lx 1 1.2 1.4 1.6 1.8 2 infinity

9.372 mm 1.654 mm

** Long term deflection :Due to shrinkage = Value of k3 Value of pt Value of pc Value of k4 Value of Ecs

k3= 0.063 pt= 0.4430769231 pc= 0.2215384615 k4= 0.2396304848 Ecs= 0.0003

ysh=(k3*k4*Ecs*lx*lx)/(D) = Deflection due to shrinkage(ysh= Due to creep = Effective modulus of elasticity Modular ratio Neutral axis Lever arm Second Moment of area of cracked section Effective second moment of area

0.917 mm

Ece = 9615.38 N/sq.mm m= 20.8 x = 22.551444582 mm z= 57.482851806 mm Icr= 1.46E+07 mm4 Ieff= 2.24E+07 mm4

y =(Alpha*w*lx*lx*lx*lx*B)/(Ec*12*Ieff) = Initial and Creep deflection due to DL using Ece = Short term deflection due to DL using Ec =

11.651 mm 7.718 mm

Ieff=

Deflection due to creep(yc =)

3.933 mm

Long term deflection =

4.850 mm

**

Total deflection(LL+SH+C)= Allowable limit (l/350) =

6.504 mm 12.857 mm SAFE

**

Total deflection(DL+LL+SH+C)= Allowable limit (l/250) =

14.222 mm 18 mm SAFE

r Discontinuous edge 275 for continuous edge

for cantilever 25 for simply ed 86 for continuous at one end 63 for fully continuous end

alpha 0.021 0.0243 0.0262 0.0273 0.028 0.0283 0.0285

2.24E+07

Our case ly/lx 1 1.2

alpha 0.021 0.0243