Structural Concrete - Hassoun

652 Chapter 17 Design of Two-Way Slabs
Thus
Let
Q =
α ec =
233E c
202.5E c
= 1.15
(
1 + 1
α ec
)
= 1 + 1
1.15 = 1.87
4. Calculate the design moments in the long direction: l 1 = 24 ft. The distribution of moments in one
panel is shown in Fig. 17.18. The interior negative moment is
[
M nt = 0.75 − 0.10
] (
M
Q 0l = 0.75 − 0.10 )
(411.4) =−286.6K⋅ ft
1.87
The positive moment is
M p =
(
0.63 − 0.28
Q
(
=
The exterior negative moment is
0.63 − 0.28
1.87
)
M 0l
)
(411.4) =197.6K⋅ ft
M ne = 0.65
Q (M 0l )=0.65 (411.4) =−143.0K⋅ ft
1.87
5. Calculate the distribution of panel moments in the transverse direction to column and middle
strips. The moments M ni , M p ,andM ne are distributed as follows (refer to Table 17.6):
a. The interior moment (M nl ) =−28 6.6 K ⋅ ft is distributed 75% for the column strip and 25%
for the middle strip.
Column strip = 0.75(−286.6) =−215 K ⋅ ft
Middle strip = 0.25(−286.6) =−71.6K⋅ ft
b. The positive moment, M p = 197.6 K ⋅ ft, is distributed 60% for the column strip and 40% for
the middle strip.
Column strip = 0.6(197.6) =118.5K⋅ ft
Middle strip = 0.4(197.6) =79.1K⋅ ft
c. The exterior negative moment, M ne =−143 K ⋅ ft, is distributed according to Table 17.5:
β t = E c C = C 2E c I s 2I s
The concrete of slab and column are the same.
I s =(20 × 12) (9.0)3 = 14,580 in. 4
12
3482
β t =
2 × 14,580 = 0.119
α f1
= E cb I b
E cs I s
= 0 α f1
l 2
l 1
= 0
l 2
l 1
= 0.83
From Table 17.5 and by interpolation between β t = 0 (percentage = 100%) and β t = 2.5 (percentage
= 100%) for β t = 0.1119, the percentage is 99%. The exterior negative moment in the
column strip is 0.99(−143.10) =−142 K ⋅ ft and in the middle strip, it is −1.10 K ⋅ ft. It is
practical to consider that the column strip carries in this case 100% of M ne =−143 K ⋅ ft.