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.
