Flange width concept in T and L beams

Concept

In a monolithic slab-beam system, the slab on either side of the beam web acts with the web in resisting bending, forming a T-beam (slab on both sides) or L-beam (slab on one side, e.g. edge beam). The compressive stress in the slab is not uniform across its width; it is highest at the web and falls away from it, because the shear that transfers compression from the web to the flange is carried by shear deformation of the slab (shear lag).

 compressive stress across flange      T-beam section
   ___                                 +------------------+  Df
  /   \___                             +----+      +------+
 /        \___                              |  bw  |
 |  web     slab edge                      |      |

For simple design, the actual variable stress is replaced by a uniform stress over a smaller effective flange width $b_f$ which gives the same total compression.

Effective flange width (IS 456 cl. 23.1.2)

• T-beam: $b_f=\dfrac{l_0}{6}+b_w+6D_f$
• L-beam: $b_f=\dfrac{l_0}{12}+b_w+3D_f$
• Isolated T-beam: $b_f=\dfrac{l_0}{\dfrac{l_0}{b}+4}+b_w$
• $b_f$ must not exceed the actual width of the flange, or the centre-to-centre spacing of beams.

Here $l_0$ is the distance between points of zero moment (equal to the effective span for a simply supported beam), $b_w$ the web width, $D_f$ the flange thickness and $b$ the actual flange width.