Structural Concrete - Hassoun

150 Chapter 3 Flexural Analysis of Reinforced Concrete Beams
3.5 Using the ACI Code requirements, calculate the design moment strength of a rectangular section that has
a width of b = 250 mm (10 in.) and an effective depth of d = 550 mm (22 in.) when f c ′ = 20 MPa(3ksi),
f y = 420 MPa (60 ksi), and the steel used is as follows:
a. 4 × 20 mm
b. 3 × 25 mm
c. 4 × 30 mm
d. 2 no. 9 bars
e. 6 no. 9 bars
3.6 A reinforced concrete simple beam has a rectangular section with a width of b = 8 in. (200 mm) and effective
depth of d = 18 in. (450 mm). At design moment (failure), the strain in the steel was recorded and was
equal to 0.0015. (The strain in concrete at failure may be assumed to be 0.003) Use f c ′ = 3ksi(20 MPa)
and f y = 50 ksi (350 MPa) for all parts.
a. Check if the section is balanced, tension controlled, or compression controlled.
b. Determine the steel area that will make the section balanced.
c. Calculate the steel area provided in the section to produce the aforementioned strains and then calculate
its moment. Compare this value with the design moment strength allowed by the ACI Code
using ρ max .
d. Calculate the design moment strength of the section if the steel percentage used is ρ = 1.4%.
3.7 A 10-ft.- (3-m)-span cantilever beam has an effective cross section (bd) of12× 24 in. (300 × 600 mm)
and is reinforced with five no. 8 (5 × 25 mm) bars. If the uniform load due to its own weight and the dead
load are equal to 685 lb/ft (10 kN/m), determine the allowable uniform live load on the beam using the
ACI load factors. Given: f c ′ = 3ksi(20MPa)andf y = 60 ksi (400 MPa).
3.8 The cross section of a 17-ft (5-m)-span simply supported beam is 10 × 28 in. (250 × 700 mm), and it
is reinforced symmetrically with eight no. 6 bars (8 × 20 mm) in two rows. Determine the allowable
concentrated live load at midspan considering the total acting dead load (including self-weight) is equal
to 2.55 K/ft (37 kN/m). Given: f c ′ = 3ksi(20MPa)andf y = 40 ksi (300 MPa).
3.9 Determine the design moment strength of the sections shown in Fig. 3.41. Neglect the lack of symmetry
in (b). Given: f c ′ = 4ksi(30MPa)andf y = 60 ksi (400 MPa).
3.10 A rectangular concrete section has a width of b = 12 in. (300 mm), an effective depth of d = 18 in.
(450 mm), and d ′ = 2.5 in. (60 mm). If compression steel consisting of two no. 7 bars (2 × 20 mm) is
used, calculate the allowable moment strength that can be applied on the section if the tensile steel, A s ,
is as follows:
a. Four no. 7 (4 × 20 mm) bars
b. Eight no. 7 (8 × 20 mm) bars
Given: f c ′ = 3ksi(20MPa)andf y = 40 ksi (300 MPa).
3.11 A 16-ft- (4.8-m-)span simply supported beam has a width of b = 12 in. (300 mm), d = 22 in. (500 mm),
d ′ = 2.5 in. (60 mm), and A ′ s = three no. 6 bars (3 × 20 mm). The beam carries a uniform dead load of
2 K/ft (30 kN/m), including its own weight. Calculate the allowable uniform live load that can be safely
applied on the beam. Given: f c ′ = 4ksi(20MPa)andf y = 60 ksi (400 MPa). (Hint: Use ρ max for the basic
section to calculate M u .)
3.12 Check the adequacy of a 10-ft- (3-m)-span cantilever beam, assuming a concrete strength of f c ′ = 4ksi
(30 MPa) and a steel yield strength of f y = 60 ksi (400 MPa) are used. The dimensions of the beam section
are b = 10 in. (250 mm), d = 20 in. (500 mm), d ′ = 2.5 in. (60 mm), A s = six no. 7 bars (6 × 20 mm),
A ′ s = twono. 5 bars (2 × 15 mm). The dead load on the beam, excluding its own weight, is equal to 2 K/ft
(30 kN/m), and the live load equals 1.25 K/ft (20 kN/m). (Compare the internal M u with the external
factored moment.)
3.13 A series of reinforced concrete beams spaced at 9 ft (2.7 m) on centers are acting on a simply supported
span of 18 ft (5.4 m). The beam supports a reinforced concrete floor slab 4 in. (100 mm) thick. If the width
of the web is b w = 10 in. (250 mm), d = 18 in. (450 mm), and the beam is reinforced with three no. 9 bars
(3 × 30 mm), determine the moment strength of a typical interior beam. Given: f c ′ = 4ksi(30MPa)and
f y = 60 ksi (400 MPa).