Assumption
1- Slab is supported on all edges e.g. with the help of beams.
2- Slab can carry any kind of loading like point load, UDL etc.
3- We know the drawing details of slab-like no. Of steel bars and type of concrete.
4- We just want to know the theoretical capacity of the slab not actually otherwise we may need to do a plate load test which is destructive in nature.
Let’s find out the capacity of the slab!
Step 1 – Find out the no. Of bars and their dimensions in the one-meter span of the slab in a shorter direction.
Step 2 – Find out the grade of concrete.
Step 3 – Using the IS 456 page 90 formula, calculate the area of steel present in tension and the thickness of the slab and thereafter find the moment of resistance of slab.
fck = Grade of concrete.
fy = Grade of steel.
B = Width of beam.
d = Effective depth of the beam.
xu = Depth of neutral axis (NA) from the top of the beam section.
xu,lim =limiting depth of neutral axis (NA) from top of beam section for balanced section.
Ast = Area of steel.
Compressive force, C = 0.36fckBxu
Tensile force, T = 0.87fyAst
Lever arm, LA = d−0.42xuLA
Moment of Resistance, MOR = C×LA = T×LAMOR
MOR = 0.36fckBxu(d−0.42xu)
MOR = 0.87fyAst(d−0.42xu)
The above are general formulas for MOR.
For under-reinforced section, xu<xu,lim
xu,lim depends on fy & d only.
Step 4 – After knowing the Moment of resistance you can find out the load on beam as you know the span of the beam because,
Moment = force × perpendicular distance.
From this, you can calculate the strength of the slab without breaking the slab.
