Design of Two Way Slab by Coefficient Method

 

Any slab having Longer and Shorter span ratio less than 1.5 will be considered as Two way slab which means both spans (Longer and Shorter) will carry the loading and both side bars will contribute as per their specific bending moments.

Example

Suppose we have a slab panel sizing 20 ft x 20ft having imposed UDL of 150 Lbs/Ft.

1) First we will find the rough thickness of slab =span/35

= 20/35= 0.571 Ft =  6.85 Inches say 7"

 

So self load of slab = Unit Volume of slab x density of RCC

=  1x1x7/12x150= 87.5 Lbs/Sft

Total UDL =      150+ 87.5 = 238 Pounds per Sq.Ft

Formulas for Bending Moment at Longer span Ly and Shorter Span Lx is as follows.

Mx= ax.w.lx.lx

My= ay.w.ly.ly

Mx= Maximum Bending Moment at Middle strip of shorter span

My= Maximum Bending Moment at Middle strip of Longer span

ax= Shorter span

ay =Longer span

ax= Co-efficient of shorter span

ay= Co-efficient of longer span

Following coefficient table may be used as per Ly/Lx Ratios.

so in our case span Ratio = 20/20 = 1 

So ax= 0.062

     ay= 0.062

So Putting values in Bending Moment formulas 

Mx= ax.w.lx.lx

0.062 x 238 x 20 x 20 x 12 = 70828 Pounds-Inch 

In above equation 12 is in inches 

My= ay.w.ly.ly

0.062 x 238 x 20 x 20 x 12 = 70828 Pounds-Inch

As per Elastic Theory Method (Using 1:2:4) concrete

Moment of resistance = Bending Moment

Moment of Resistance in Elastic theory method 

= 184.b.d1.d1

where b is unit width of slab

d1 = Effective depth of slab (depth without covers)

Putting values in above equation 

70828= 184 x 12 x d1 xd1

d1 = 5.75 inch for Mx and My 

So adding 1/2" concrete cover on top and bottom overall depth will be 6.75 Inches

Ast = Bending Moment /Fst x Lever Arm

where Ast = Area of steel in tension zone

Fst = Factored Tensile stress of steel (which is 20,000 Psi) 

Factor of safety is 3 

Lever arm = 0.857 x Effective Depth

Putting Values in Above equation 

Ast = 70828/ 20000x0.857x5.75  = 0.718 Sq.Inch

Spacing of Bars = (Area of bar x 12) /0.718 

Using 1/2 inch dia bar 

Spacing = (0.196 x 12 )/0.718 = 3.27 say 3.25 Inch c/c 

So 1/2" dia bar will be used @ 3.25 inch center to center both ways and slab thickness will be 6.75 inch using (1:2:4) concrete.