# Design of T and L Beam in Flexure.

The T or L Beam gets its name when the slab and beam produce the cross sections having the typical T and L shapes in a monolithic reinforced concrete construction.

In casting of reinforced concrete floors/roofs, forms are built for beam sides, the underside of slabs, and the
entire concrete is mostly poured at once, from the bottom of the deepest beam to the top of the slab.

Positive Bending Moment

• In the analysis and design of floor and roof systems, it is common practice to assume that the monolithically placed slab and supporting beam interact as a unit in resisting the positive bending moment.
• As shown, the slab becomes the compression flange, while the supporting beam becomes the web or stem.

Negative Bending Moment

In the case of negative bending moment, the slab at the top of the stem (web) will be in tension while the bottom of the stem is in compression. This usually occurs at interior support of continuous beam.

# ACI Code Provisions for T and L Beams

• For T and L beams supporting monolithic or composite slabs, the effective flange width bf shall include the beam web width bw plus an effective overhanging flange width in accordance with ACI Table 6.3.2.1

• Calculation of Effective Flange Width (bf) (ACI 6.3.2.1)

• Where bw is the width of the beam, h is the slab thickness, sw is the clear distance to the adjacent beam and ℓn is the clear length of beam.
• Calculation of Effective Flange Width (bf) (ACI 6.3.2.1)

Where bw is the width of the beam, h is the slab thickness, sw is the clear distance to the adjacent beam and ℓn is the clear length of beam.

# Design Cases

• In designing a T-Beam for positive bending moment, there might exist two conditions:
• Condition 1. The depth of the compression block may be less than or equal to the slab depth i.e. flange thickness (a ≤ h)
• In such a condition the T-Beam is designed as rectangular beam for positive
bending with the width of compression block equal to bf.

Condition 2. The compression block may cover the flange and extend into the web (a ˃ h) In such condition the T-Beam is designed as true T-beam.

# Design of Rectangular T-beam

Flexural Capacity
When a ≤ h

# Practical Example

The roof of a hall has a 5” thick slab supported on beam having 30 feet c/c and 28.5 feet clear span. Adjacent beams are having 9 feet clear distance and have been cast monolithically with slab. Overall depth of beam
(including slab thickness) being 24 in and width of beam web being 14 in. Calculate the steel reinforcement area for the beam for a total factored load (including self weight of beam) of 3 k/ft. Use fc′ = 3 ksi and fy = 60 ksi.

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