Structural Concrete - Hassoun

3.15 Analysis of T- and I-Sections 129
Figure 3.29
Effective flange width of T-beams.
A T-shaped or I-shaped section may behave as a rectangular section or a T-section. The two
cases are investigated as follows.
3.15.3 T-Sections Behaving as Rectangular Sections
In this case, the depth of the equivalent stress block ‘a’ lies within the flange, with extreme position
at the level of the bottom fibers of the compression flange (a ≤ t). When the neutral axis lies within
the flange (Fig. 3.30a), the depth of the equivalent compressive distribution stress lies within the
flange, producing a compressed area equal to b e a. The concrete below the neutral axis is assumed to
be ineffective, and the section is considered singly reinforced, as explained earlier, with b replaced
by b e . Therefore,
a =
A s f y
0.85f cb ′ (3.58)
e
and
(
φM n = φA s f y d − a )
(3.59)
2
If the depth a is increased such that a = t, then the factored moment capacity is that of a singly
reinforced concrete section:
(
φM n = φA s f y d − t )
(3.60)
2
In this case
t =
A s f y
0.85f cb ′ or A s = 0.85f cb ′ e t
(3.61)
e f y
In this analysis, the limit of the steel area in the section should apply: A s ≤ A s,max ,andε t ≥ 0.005.
3.15.4 Analysis of a T-Section
In this case the depth of the equivalent compressive distribution stress lies below the flange; consequently,
the neutral axis also lies in the web. This is due to an amount of tension steel A s more