T-Section:

The method of determining the shear stress distribution in T-sections is same to that of I-section. As the T-section is not symmetrical around the neutral axis, the shear stress distribution also shall not be symmetrical.

Example

A T-section contains a flange of size 150 mm × 50 mm & web of size 50 mm × 150 mm. This section is subjected to a vertical shear force of 100 kN.

Determine the maximum shear stress & draw the shear stress distribution diagram along with values at vital points. Centroid of section is 125 mm from the bottom face & moment of inertia around the centroidal axis is 5312.5 × 104 mm⁴.

Beam Cross-section                              Shear Stress Distribution              

Solution

Maximum shear stress takes place at the neutral axis.

Therefore,        τ_max = ( F/ Ib) × A y

=  (100 × 1000 / 5312.5 × 10⁴ × 50)[(150 × 50) × 50 + (50 × 25) × 12.5]

= 14.71 N/mm²

In the flange shear stress at the junction of flange & web,

 = (100 × 1000/5312.5 × 10⁴ × 150) × (150 × 50 × 50)

 = 4.71 N/mm²

In the web shear stress at the junction of flange & web,

= (100 × 1000/5312.5 × 10⁴ × 50) × (150 × 50 × 50)

= 14.12 N/mm²

The shear stress distribution is illustrated in Figure.