T beam design – Parts of T Beam with Numerical Calculation

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T beam design includes the steel and thickness required to bear the load applied on it. So, before designing T beam, we must know some important terms and parts of T beam. Let’s start.

What is T – beam?

Slabs and beams are cast monolithically in RCC construction. In this construction, a portion of the slab act integrally with the beam and bends along with the beam under the loads. This phenomenon is seen in the beams supported slab system as shown in the figure.

The part of the slab which carries the load and connected with the beam as a single part of the L- beam or T- Beam is known as the flange of the T beam.

The portion of beam below the flange is called as web of the beam.

The middle beams supporting the slab are called as T-beam and the end beams shaping like letter L are known as L-beams.

T beam design - Parts of T Beam with Numerical Calculation

The flange of the beam contributes to resisting compression by adding more areas of concrete in the compression zone. The results in increasing moment of resistance of the beam section.

The concrete area of the flange is to be neglected (cracked) and the beam is treated as a rectangular beam if the flange is located in the tension zone.

Terms used in T-Beams

  1.  Breadth of web (bw)

It should be sufficient enough to accommodate the tensile reinforcement properly. The ratio of the width of the web to the depth of the web is kept as 1/3 to 2/3.

  • Thickness of the flange (Df)

The thickness of the flange of T beam is equal to the thickness or depth of the slab forming the flange of the beam.

  • Overall depth of the beam (D)

Overall depth of a flanged beam is equal to the sum of the depth of flange (Df) and depth of the web (dw).

T beam design - Parts of T Beam with Numerical Calculation

Examples of T beam design

Q) A T-beam has a flanged width of 1200 mm and flanged thickness being 100 mm. Steel reinforcement of area 1272 mm2 is placed at an effective depth of 400 mm. The stresses in concrete and steel shall not exceed 5 N/mm2. Find moment of resistance of beam. Take m = 18.67

Solution;

Given:

Critical neutral axis (nc)

Actual neutral axis (assuming n>Df)

T beam design - Parts of T Beam with Numerical Calculation

n<nc , hence the section is under reinforced and  st = 230 N/mm2.

  • Determining stress ( cbc and c )
  • Moment of resistance (Mr)

Moment of resistance (Mr) of the given section, without taking into account the compression in the web ( breadth of the web is not given) is calculated as follows:

Q) Determine the area of compression and tension steel for a rectangular beam of 300 mm x 500 mm effective depth by working stress method. If it is subjected to 95 KNm moment using M20 concrete and Fe 415 steel. – (T beam design)

Solution:

Size of beam = 300 x 500 mm effective

       M = 95 KNm

  • Design constants for M20 and Fe 415

k = 0.29

            j = 0.9

            R = 0.91 N/mm2

Critical neutral axis, n = kd = 0.29 x 500  = 145 mm

  • Moment of resistance of balanced section (M1)

M1 = Rbd2

      = 0.91 x 300 x 5002

M1 = 68.25 KNm

M2 = M – M1

       = 95 – 68.25

      = 26.75 KNm

  • Area of steel (Ast) in tension
T beam design - Parts of T Beam with Numerical Calculation
  • Area of steel in compression (Asc)
T beam design - Parts of T Beam with Numerical Calculation

Now, use steel rod according to area of steel required as calculated above.

I hope this article on T beam design remains helpful for you.

Happy Learning – Civil Concept

Contributed by,

Civil Engineer – Pradeep Thakur

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