Structural Concrete - Hassoun

3.15 Analysis of T- and I-Sections 131
Figure 3.32
T-section analysis.
The analysis of a T-section is similar to that of a doubly reinforced concrete section, considering
an area of concrete (b e − b w )t as equivalent to the compression steel area A ′ s. The analysis is
divided into two parts, as shown in Fig. 3.32:
1. A singly reinforced rectangular basic section, b w d, and steel reinforcement A s1 .Thecompressive
force, C 1 , is equal to 0.85 f ′ cab w , the tensile force, T 1 , is equal to A s1 f y , and the moment
armisequaltod − a/2.
2. A section that consists of the concrete overhanging flange sides 2 × [(b e − b w )t]/2 developing
the additional compressive force (when multiplied by 0.85 f ′ c ) and a moment arm equal to
d − t/2. If A sf is the area of tension steel that will develop a force equal to the compressive
strength of the overhanging flanges, then
A sf f y = 0.85f ′ c(b e − b w )t
A sf = 0.85f ′ ct(b e − b w )
f y
(3.62)
The total steel used in the T-section A s is equal to A s 1 + A sf ,or
A s1 = A s − A sf (3.63)
The T-section is in equilibrium, so C 1 = T 1 , C 2 = T 2 ,andC = C 1 + C 2 = T 1 + T 2 = T. Considering
equation C 1 = T 1 for the basic section, then A s1 f y = 0.85 f ′ cab w or (A s − A sf )f y = 0.85
f ′ cab w ; therefore,
a = (A s − A sf )f y
0.85f ′ cb w
(3.64)