Civil Engineering Reference
In-Depth Information
For other loading conditions it may be assumed (according to ACI Section
13.7.6.3) that maximum positive moment at the midspan of a panel will occur when
three-fourths of the full factored live load is placed on the panel in question and on al-
ternate spans. It may be further assumed that the maximum negative moment at a sup-
port will occur when three-fourths of the full factored live load is placed only on the
adjacent spans.
The Code permits the use of the three-fourths factor because the absolute maximum
positive and negative moments cannot occur simultaneously under a single loading condi-
tion and also because some redistribution of moments is possible before failure will occur.
Although some local overstress may be the result of this procedure, it is felt that the ulti-
mate capacity of the system after redistribution will be sufficient to resist the full factored
dead and live loads in every panel.
The moment determined as described in the last paragraph may not be less than mo-
ments obtained when full factored live loads are placed in every panel (ACI 13.7.6.4).
16.11
ANALYSIS OF TWO-WAY SLABS WITH BEAMS
In this section the moments are determined by the direct design method for an exterior
panel of a two-way slab with beams. It is felt that if you can handle this problem, you can
handle any other case that may arise in flat plates, flat slabs, or two-way slabs with beams
using the direct design method.
The requirements of the Code are so lengthy and complex that in Example 16.4,
which follows, the steps and appropriate Code sections are spelled out in detail. The prac-
ticing designer should obtain a copy of the
CRSI Design Handbook
, because the tables
therein will be of tremendous help in slab design.
EXAMPLE 16.4
Determine the negative and positive moments required for the design of the exterior panel of the
two-way slab with beam structure shown in Figure 16.17. The slab is to support a live load of 120
psf and a dead load of 100 psf including the slab weight. The columns are 15 in.
15 in. and 12 ft
long. The slab is supported by beams along the column line with the cross section shown. Deter-
mine the slab thickness and check the shear stress if
c
3000 psi and
f
y
60,000 psi.
f
SOLUTION
1.
Check ACI Code limitations (13.6.1). These conditions are met.
2.
Minimum thickness as required by Code (9.5.3):
(a)
Assume
h
6 in.
(b)
Effective flange projection of column line beam as specified by the Code (13.2.4)
4
h
f
(4)(6)
24
or
h
h
f
20
6
14
(c)
Gross moments of inertia of T beams. The following values are the gross moments of
inertia of the edge and interior beams computed, respectively, about their centroidal axes. Many de-
signers use approximate values for these moments of inertia,
I
s
, with almost identical results for slab
thicknesses. One common practice is to use 2 times the gross moment of inertia of the stem (using a
