Structural Concrete - Hassoun

136 Chapter 3 Flexural Analysis of Reinforced Concrete Beams
4. Check that A s > A s,min , ρ min = 0.00333:
A s,min = 0.00333 × 10 × 17 = 0.57 in. 2
5. Calculate φ M n using Eq. 3.65:
[ (As )
φM n = φ − A sf fy
(d − 1 )
2 a + A sf f y
(d − 1 )]
2 t
[ (
= 0.9 2.13 × 60
17 − 4.3
2
= 4947 K ⋅ in. = 412.3K⋅ ft
)
(
+ 3.87 × 60 17 − 3 )]
2
Another approach to check whether a ≤ t is to calculate the tension force, T = A s f y , and compare
it to the compressive force in the total flange (Fig. 3.34):
T = A s f y = 60 × 60 = 360 K
C = 0.85f c ′ tb e = 0.85 × 3.5 × 3 × 36 = 321.3K
Since T exceeds C,thena ≤ t, and the section acts as a T-section.
An additional area of concrete should be used to provide the difference of (360 −321.3) =
38.7 K. This area has a width of 10 in. and a depth of y. Therefore,
b w y(0.85f c ′ )=38.7 K or 10(y)(0.85 × 3.5) =38.7K
where y = 1.3 in., and a = y + t = 1.3 +3 = 4.3 in., as calculated earlier.
3.16 DIMENSIONS OF ISOLATED T-SHAPED SECTIONS
In some cases, isolated beams with the shape of a T-section are used in which additional compression
area is provided to increase the compression force capacity of sections. These sections are
commonly used as prefabricated units.
The ACI Code, Section 6.3.2.2, specifies the size of isolated T-shaped sections as follows:
1. Flange thickness, t, shall be equal to or greater than one-half of the width of the web, b w .
2. Total flange width b shall be equal to or less than four times the width of the web, b w
(Fig. 3.35).
Figure 3.35
Isolated T-shaped sections.