How to calculate effective depth of beam and slab ,hi guys in this articles we know about what is definition of effective depth of beam and slab and also know about what is effective depth of simply supported beam and cantilever beam.
We know that beam and slab is horizontal flexural member of building construction in which beam and slab structure member undergoes compression and tension both.
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Upper concrete fibre of slab and beam is known as compression fibre and reinforcement provided in compression fibre is known as compression Steel and lower concrete fibre of beam and slab is known as tension fibre and reinforcement provided in tension fibre is known as tension Steel.
due to flexural nature it undergoes only shear stress and bending moment not buckling. Effective depth of beam is quite helpful in calculating in structural beam design.
And in this article we discuss about how to calculate effective depth of beam and slab.
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What is definition of effective depth of beam and slab
Effective depth of the beam and slab is the distance between extreme compressive concrete fibre to the centroid of tension reinforcement in section under flexural condition.
And in another words it is described as distance from the centroid of tension Steel to theoutermost face of compression fibre.
Effective depth of slab is the distance from the compression face to the centre of the tensile steel when an element is subjected to a bending moment.
How we calculate effective depth of beam
Effective depth of beam is calculated over all deep of beam minus effective cover of beam.
if d is effective depth of beam and their deep is h and there effective cover is Ce than
effective depth = total deep _ effective cover
that is d = h _ Ce
Now discuss about what is effective cover. Effective cover is distance between centroid of tension Steel to bottom extreme face of concrete tension fibre where maximum tension is present. So effective cover is sum of nominal cover of tension concrete fibre and half of diameter of Steel bar.
effective cover = nominal cover + 1/2 dia of main reinforcement
That is Ce = Cn + dia/2
Important point is noted here that according to IS code 456- 2000 clear cover and concrete cover both technical term are omitted and this is deleted and in place of clear cover and concrete cover according to IS code only nominal cover and effective cover is being used today.
nominal cover is distance from extreme face of tension fibre to the The outer most face of tension Steel including shear link or stirrups. So do not confuse with clear cover or concrete cover or nominal cover all are same.
How to calculate effective depth of simply supported beam
We know that simply supported beam has two support end either it will be wall or column. And if vertical load is acting on simply supported beam in downward direction resulting bending moment.
That’s undergo positive bending moment sagging at L/2 span of beam and negative bending moment hogging at column beam Junction. Due to sagging bending moment there bottom face of concrete comes in tension zone and offer face of concrete fibre comes in compression zone and is steel present in tension zone is tension steel and the Steel present in compression fibre is known as compression Steel.
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So in the case of simply supported beam tension Steel in bottom face that’s why we calculate effective depth is distance between top extreme compressive fibre to the centroid of tension Steel of tension concrete fibre in downward direction. And their effective cover is measured from extreme face of bottom tension concrete fibre to the centroid of tension Steel in upward direction.
If total deep of simply supported beam is presented by ” h ” and their effective cover is “Ce ” And dia of tension steel is ” T20″ and there nominal cover represented by Cn
We have h = 600 mm
dia of reinforcement = T20
Nominal cover = 40 mm
effective depth = total deep _ effective cover
that is d = h _ Ce
And
effective cover = nominal cover + 1/2 dia of main reinforcement
That is Ce = Cn + dia/2
Value of Ce = 40 mm + 20/2 = 50 mm
Put this value of nominal cover in
effective depth d = h _ Ce
d = 600 mm _ 50 mm
Effective depth = 550 mm
How to calculate effective depth of cantilever beam
We know that cantilever beam has one support and other free end either support will be wall or column. And if vertical load is acting on cantilever beam in downward direction resulting bending moment.
That’s undergo negative bending moment hogging at L/2 span of beam and positive bending moment sagging at column beam Junction. Due to hogging bending moment at L/2 span of cantilever beam their upper face of concrete comes in tension zone and bottom face of concrete fibre comes in compression zone and is steel present in tension zone is tension steel and the Steel present in compression fibre is known as compression Steel.
So in the case of cantilever beam tension Steel in upper face that’s why we calculate effective depth is distance between bottom extreme compressive fibre to the centroid of tension Steel of tension concrete fibre in upward direction. And their effective cover is measured from extreme face of upper tension concrete fibre to the centroid of tension Steel in downward direction.
If total deep of cantilever beam is presented by ” h ” and their effective cover is “Ce ” And dia of tension steel is ” T12″ and there nominal cover represented by Cn
We have h = 300 mm
dia of reinforcement = T12
Nominal cover = 25 mm
effective depth = total deep _ effective cover
that is d = h _ Ce
And
effective cover = nominal cover + 1/2 dia of tension reinforcement
That is Ce = Cn + dia/2
Value of Ce = 25 mm + 12/2 = 31 mm
Put this value of nominal cover in
effective depth d = h _ Ce
d = 300 mm _ 31 mm
Effective depth of cantilever beam in upward direction = 269 mm
How to calculate effective depth of slab
Slab is also flexural concrete structure member and function as same as simply supported beam and their bending moment in downward direction. When load and live load acting vertically on slab in downward direction slab transfer its own load to the vertically to the beam.
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Slab undergoes bending moment that is sagging at the midpoint of Span so upper concrete fibre of slab in compression zone and their steel is known as compression Steel and bottom part of concrete fibre of slab in tension zone and there is steel present in tension zone is known as tension Steel.
So in the case of simply supported slab tension Steel in bottom face that’s why we calculate effective depth is distance between top extreme compressive fibre of slab to the centroid of tension Steel of tension concrete fibre in downward direction.
And their effective cover is measured from extreme face of bottom tension concrete fibre to the centroid of tension Steel in upward direction.
If total deep of simply supported slab is presented by ” h ” and their effective cover is “Ce ” And dia of tension steel is ” T12″ and there nominal cover represented by Cn
We have h = 150 mm
dia of reinforcement = T12
Nominal cover = 20 mm
effective depth = total deep _ effective cover
that is d = h _ Ce
And
effective cover = nominal cover + 1/2 dia of Tension reinforcement
That is Ce = Cn + dia/2
Value of Ce = 20 mm + 12/2 = 26 mm
Put this value of nominal cover in
effective depth d = h _ Ce
d = 150 mm _ 26 mm
Effective depth of simply supported slab is = 124 mm