Depth of the Slab as per ACI 318-05

As slab depth directly affects the dead load on the beam, we should determine it more precisely in intial trial

Preliminary thickness of the slab; Slab panel C,D-1,2
ACI318-05; Cl 9.5.3.3

 
 
 
 
 
 
 
 
 
 
Where
αf = (Eb*Ib)/(Es*Is); Eb =Es for same Concrete grade

Ib =Moment  of Inertia of beam, Is = Moment of Inertia of tributary slab
αfm = average of all αf of beam on the boundary of slab

for αfm less than and equal to 0.2 slan behaves as flat slab and ACI 318-05; Cl 9.5.3.2 will be applicable
Tributary Slab width for panel C,D-1,2

Beam to slab stiffness ratios

Beam width, B=230mm

Beam Effective Depth, d=300 mm
MOI of Beam, Ib =Bd3/12 =0.23*0.3^3/12=0.000518 m4

For Beam BM1; ls = 3.6 m; Is =3.6*0.125^3/12= 0.000586 ; αf1= 0.000518/0.000586= 0.8832

For Beam BM2; ls = 3.638 m; Is =3.638*0.125^3/12= 0.000592 ; αf2= 0.000518/0.000592= 0.8739

For Beam BM3; ls = 1.95 m; Is =1.95*0.125^3/12= 0.000317 ; αf3= 0.000518/0.000317= 1.63

For Beam BM4; ls = 2.1 m; Is =2.1*0.125^3/12= 0.000342 ; αf4= 0.000518/0.000342= 1.514

Average αfm =(0.8832+0.8739+1.63+1.514)/4 =1.225>0.2, <2=> ACI318-05; cl9.5.3.3 b is valid

Thickness of slab
αfm = 1.225

Long clear span/short clear span,β =(4.2-0.23)/(3.9-0.23)= 1.08
ln= shorter clear span =3.9-0.23=3.67 m

ACI318-05; cl9.5.3.3b:

Thickness of slab, h= {97.2,125}max =125 mm

Estimating Beam Depth for Initial trial

Deflection criteria: Use simplified form of IS456,2000 cl23.2.1


Span/deff= BV*mft*mfc*mff

For Both End Simply supported , Basic Value(BV) =26

mft= 0.8 for Assumed 2.5% tension steel

Assume; mfc = 1.25 for 1% Compression steel

Assume ;mff= 0.8 for web width/ flange width<0.3

Span/depth = 20*0.8*1.25*0.8=16 (approx), for simply supported

Span/depth = 26*0.8*1.25*0.8=20( approx), for both end continuous

Span/depth= 23*0.8*1.25*0.8=18( approx), for one end simply supported and one end continuous

Sample Calculation;
Beam span=4200mm
Boundary Condition; one end simply supported other end continuous
deff= span/18= 4200/18= 233.33 mm


Overall depth = deff+(assumed bar dia)/2+Clear cover = 233.33+25/2+25= 270.83 Assume 300mm ( 12”)

Ductile Detailing criteria( IS13920;1993)
 
The spacing of hoops over a length of 2d at either end of a beam


S<[ deff/4, 8*φsmall longitudinal bar, 24*φhoop, 300 ]min

Sample Calculation

Assume, s =75 mm, φsmall longitudinal bar =12mm, 24*φhoop =8mm


Effective depth of the beam/4 =75 mm


Effective depth of the beam =300mm


Overall depth of the beam = 300+25/2+25=337.5 =350 mm (approx round off value)


Check for S(75mm)<[ (deff/4=75), (8*φsmall longitudinal bar =96), (24*φhoop =192), 300 ]min=75mm; Satisfied

Conclusion: Thumb Rule
Span/depth = 16 (approx), for simply supported

Span/depth = 20( approx), for both end continuous
Span/depth= 18( approx), for one end simply supported and one end continuous