How do you calculate the neutral axis of reinforced concrete slab?

Answer 1

Concrete slabs should be designed to fail under rebar yield as opposed to concrete crushing. So assuming a rebar yielding scenario the first step is to determine the maximum load which can be sustained by the tension rebar as follows,

0.87*Fy gives the failure maximum stress in the steel, which can then be multiplied by the total area of rebar to give the force of the steel in tension. where Fy is the yield strength of the steel. (typical value of Fy is say 500Mpa)

Next it is assumed that the slab is in a state of static equilibrium i.e. not accelerating off in any direction!

For this to happen the force in the concrete must = the force in the steel,

Fst = Fcc = 0.567*Fck*A

Fst = force of the steel in tension (calculated above)

Fcc = force of concrete in compression = maximum sustainable Force of steel in tension

Where Fck = concrete compressive strength,

and A = area of a simplified stress block,

limiting the depth of the stress block to 0.8x results in ;

Fcc = 0.567*Fck*0.8x*B

where x = depth to neutral axis

B = breadth of slab

Rearranging for x gives

X = (Fcc/(0.567*Fck*B))/0.8