Structural Concrete - Hassoun

170 Chapter 4 Flexural Design of Reinforced Concrete Beams
Calculate ρ 1 using M u1 , b w ,andd in Eq. 4.2 and determine A s1 = ρ 1 b w d:
Total A s = A s1 + A sf
Then check that A s ≤A s,max , as explained in Section 3.15. Also check that ρ w = A s /(b w d)
≥ρ min .
d. If a = t, then A s = φ(0.85f ′ c)bt∕f y .
2. When d and A s are not known, the design may proceed as follows:
a. Assume a = t and calculate the amount of total steel, A sft , needed to resist the compression
force in the whole flange, bt:
A sft = (0.85f ′ c)bt
f y
(4.10)
b. Calculate d based on A sft and a = t from the equation
M u = φA sft f y
(
d − 1 2 t )
(4.11)
If the depth, d, is acceptable, then A s = A sft and h = d + 2.5 in. for one row of bars or
h = d + 3.5 in. for two rows of bars.
c. If a new d 1 is adopted greater than the calculated d, then the section behaves as a rectangular
section, and ρ can be calculated using Eq. 4.2; A s = ρbd < A sft .
d. If a new d 2 is adopted that is smaller than the calculated d, then the section will act as a
T-section, and the final A s will be greater then A sft . In this case, proceed as in step 1(c) to
calculate A s .
Example 4.7
The T-beam section shown in Fig. 4.7 has a web width, b w , of 10 in., a flange width, b, of 40 in., a flange
thickness of 4 in., and an effective depth, d, of 14.5 in. Determine the necessary reinforcement if the
applied factored moment is 3350 K⋅in. Given: f c ′ = 3ksi and f y = 60 ksi.
Solution
1. Check the position of the neutral axis; the section may be rectangular. Assume the depth of compression
block a is 4 in.; that is, a = t = 4in.Then
(
φM n = φ(0.85f c ′ )bt d − 1 )
2 t = 4590K ⋅ in. >M u = 3350K ⋅ in.
Figure 4.7
Example 4.7: T-section.