Structural Concrete - Hassoun

Problems 185
No. M u
(K⋅ft) b (in.) b w
(in.) t (in.) d (in.) Notes
a 394 48 14 3 18.5
b 800 60 16 4 19.5
c 250 44 15 3 15.0
d 327 50 14 3 13.0
e 577 54 16 4 18.5
f 559 48 14 4 17.5
g 388 44 12 3 16.0
h 380 46 14 3 15.0
i 537 60 16 3 16.5
j 515 54 16 3 17.5
k 361 44 15 3 15.0
l 405 50 14 3 15.5
m 378 44 16 3 — Let a = t
n 440 36 16 4 — Let a = t
o 567 48 12 3 — Let A s = 6.0 in. 2
p 507 46 14 3 — Let A s = 7.0 in. 2
For problems in SI units, 1 in. = 25.4 mm, 1 ksi = 6.9 MPa (N/mm 2 ),
and 1 M u
(K⋅ft) = 1.356 kN⋅m.
4.4 Design a singly reinforced rectangular section to resist a factored moment of 232 K ⋅ ft (320 kN⋅m) if
f c ′ = 4ksi(28MPa),f y = 60 ksi (420 MPa), and b = 10 in. (250 mm) using (a) ρ max ,(b)ρ = 0.016, and (c)
ρ = 0.012.
4.5 Design a singly reinforced section to resist a factored moment of 186 K ⋅ ft (252 kN ⋅ m) if b = 12 in.
(275 mm), d = 20 in. (500 mm), f c ′ = 3ksi(20 MPa),andf y = 40 ksi (300 MPa).
4.6 Determine the reinforcement required for the section given in Problem 4.5 when f c ′ = 4ksi(30 MPa) and
f y = 60 ksi (400 MPa).
4.7 A simply supported beam has a 20-ft (6-m) span and carries a uniform dead load (DL) of 800 lb/ft (12
kN/m) and a concentrated live load (LL) at midspan of 9 kips (40 kN) (Fig. 4.14). Design the beam if
b = 12 in. (300 mm), f c ′ = 4ksi(30 MPa),andf y = 60 ksi (400 MPa). (Beam self-weight is not included in
the dead load.)
4.8 A beam with a span of 24 ft (7.2 m) between supports has an overhanging extended part of 8 ft (2.4 m)
on one side only. The beam carries a uniform dead load of 2.3 K/ft (30 kN/m) (including its own weight)
and a uniform live load of 1.3 K/ft (18 kN/m) (Fig. 4.15). Design the smallest singly reinforced rectangular
section to be used for the entire beam. Select steel for positive and negative moments. Use
f c ′ = 4ksi(30 MPa), f y = 60 ksi (400 MPa), and b = 12 in. (300 mm). (Determine the maximum positive
and maximum negative moments by placing the live load once on the span and once on the overhanging
part.)
Figure 4.14 Problem 4.7.