Structural Concrete - Hassoun

624 Chapter 17 Design of Two-Way Slabs
2. The gross moment of inertia of the beam, I b , is calculated for the section shown in Fig. 17.7b,
which is made up of the beam and the extension of the slab on each side of the beam x = y
but not more than four times the slab thickness. Assume h = 7 in., to be checked later; then
x = y = 22 − 7 = 15 in. < 4 × 7 = 28 in. Therefore, b e = 16 + 2 × 15 = 46 in., and the T-section is
shown in Fig. 17.7c. Determine the centroid of the section by taking moments about the top of
the flange:
Area of flange = 7 × 46 = 322 in. 2
Area of web = 16 × 15 = 240 in. 2
Total area = 562 in. 2
(322 × 3.5)+240 ×(7 + 7.5) =562y
y = 8.20 in.
[ ]
46
I b =
12 (7)3 + 322 ×(4.7) 2
[ 16(15)
3
]
+ + 240(7.5 − 1.2) 2 = 22,453 in. 4
12
3. The moment of inertia of the slab in the long direction is I s = (bh 3 )/12, where b = 20 ft and h = 7in.
I s =
(20 × 12)(7)3
12
= 6860 in. 4
α f 1 (in the long direction) = EI b
EI s
= 22,453
6860 = 3.27
4. The moment of inertia of the slab in the short direction is I s = (bh 3 )/12 where b = 24 ft and h = 7in.
5. α fm is the average of α f1 and α f2 :
I s =
(24 × 12)(7)3
12
= 8232 in. 4
α f 2 (in the short direction) = EI b
EI s
= 22,453
8232 = 2.72
3.27 + 2.72
α fm = = 3.23 > 2
2
6.
20
24 −
12
β = = 22.33
20 − 20 18.33 = 1.22
12
7. Determine Min. h using Eq. 17.2 (l n = 22.33 ft):
(22.33 × 12)(0.8 + 0.005 × 60)
h =
36 +(9 × 1.22)
A slab thickness of 6.5 in. is adequate.
= 6.27 in. >3.5in.
17.7 SHEAR STRENGTH OF SLABS
In a two-way floor system, the slab must have adequate thickness to resist both bending moments
and shear forces at the critical sections. To investigate the shear capacity of two-way slabs, the
following cases should be considered.