Structural Concrete - Hassoun

CHAPTER4
FLEXURAL
DESIGN OF
REINFORCED
CONCRETE
BEAMS
Reinforced concrete office building, Amman, Jordan.
4.1 INTRODUCTION
In the previous chapter, the analysis of different reinforced concrete sections was explained. Details
of the section were given, and we had to determine the design moment of the section. In this chapter,
the process is reversed: The external moment is given, and we must find safe, economic, and practical
dimensions of the concrete section and the area of reinforcing steel that provides adequate
internal moment strength.
4.2 RECTANGULAR SECTIONS WITH TENSION REINFORCEMENT ONLY
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From the analysis of rectangular singly reinforced sections (Section 3.9), the following equations
were derived for tension-controlled sections, where f c ′ and f y are in ksi:
f ′ ( )
c 87
ρ b = 0.85β 1 (3.18)
f y 87 + f y
For f y = 60 ksi,
Also,
ρ max = ρ b
( 0.003 + fy ∕E s
0.008
)
ρ max = 0.63375ρ b (or 0.634ρ b )
⎧0.5474ρ ⎪⎨⎪⎩ b
ρ max 0.5905ρ b
0.6983ρ b
for f y = 40 ksi
for f y = 50 ksi
for f y = 75 ksi
(3.31)