This document discusses T-beams, which are more suitable than rectangular beams in reinforced concrete. There are two types of T-beams: monolithic and isolated. It provides notations and code recommendations for T-beams from IS: 456. There are three cases for finding the depth of the neutral axis in a T-beam: when it lies in the flange, in the rib, or at the junction. An example problem is worked through to find the moment of resistance for a given T-beam section using the provided concrete and steel properties.

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T-Beams

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Strictly rectangular beams are uncommon in reinforced concrete. T-Beams are more
suitable than rectangular beams. There are two types of T-Beams which are depending upon
the mode of casting. One of them is Monolithic T-Beam and another is Isolated T-Beam.
1. Monolithic T-Beams: A such type of beam which constructed by moulding a
rectangular beam and slab together. It looks like a rectangular beam supporting slab.
2. Isolated T-Beams: An Isolated T-Beam is such type of beam in which flange of T-
Beam not connected with the slab. In this type of beam T-Beam and slab didn’t cast
at same time.

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Notations for T-Beam:
cbc = Allowable stress in concrete in bending in compression in direct stress.
st = Allowable stress in steel in bending in tension in direct stress.
σsc = Allowable stress in steel in bending in compression in direct stress.
σy = Characteristic strength of steel.
σck = Characteristic strength of concrete.
Ast = Area of steel in tension zone.
ECC = effective concrete cover
CCC = clear concrete cover

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I.S: 456 Code Recommendations:
From IS: 456, (page no 37)
Effective Flange width for monolithic T-Beam
Effective Flange width for Isolated T-Beam

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To find depth of Neutral axis of T-Beam:
There are three cases arise:
1. N.A. may lie in Flange.
2. N.A. may lie in Rib.
3. N.A. may lie at junction of Flange and Rib.
Case 1. N.A. lies in Flange:
Area moment of compression zone = Area moment of tension zone
⇒
The above equation will give the value of Actual Neutral axis
Depth of critical Neutral Axis:
Compare Value of
If
If
If

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Case 2. N.A. lies in Rib:
There are two sub-cases arises,
Sub-case 1. We consider concrete of rib as active concrete along with Flange.
Sub-case 2. We consider only concrete of Flange as active concrete.
Depth of Actual NA for Sub-case 1.
Depth of Actual NA for Sub-case 2.
Depth of critical Neutral Axis:
Moment of resistance for sub-case 2:
If
If
If

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Liver arm of T-beam:
From geometry…
Similarly for stress diagram:

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Putting the value of
⇒
⇒
⇒
Case 3. N.A. lies at junction of flange and rib:
This case will be similar as case 1.

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Example 1: A T- beam section has a flange width of 100 cm, flange thickness of 12 cm, width
of web is 25 cm and effective depth of 45 cm. it is provided with a tension reinforcement of
area 4600 mm2
. Find the moment of resistance using M20 concrete and Fe250 grade of steel.
[BNMU 2011 (A)]
Sol:
Given Data:
To find depth of actual NA (let us suppose NA to lie in Flange):

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⇒
⇒
Here
Now suppose NA lie in Web and concrete of web not considered.
⇒
⇒
To find depth of Critical NA:
To find Moment of Resistance (MR):
2

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CASE –II Suppose NA lies in rib and Rib compression also consider.
Determination of Actual NA:
⇒
⇒
Depth of Critical NA,
C1 = Compressive force taken by flange,
2
C2 = Compressive force taken by rib, 2

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Determination of depth of resultant forces:
Determination of MR: