Page 209 - Civil Engineering Formulas

144 CHAPTER FIVE

In both methods, a flat slab is considered to consist of strips parallel to column
lines in two perpendicular directions. In each direction, a column strip spans
between columns and has a width of one-fourth the shorter of the two perpendic-
ular spans on each side of the column centerline. The portion of a slab between
parallel column strips in each panel is called the middle strip (see Fig. 5.3).

Direct Design Method
This may be used when all the following conditions exist:

The slab has three or more bays in each direction.
Ratio of length to width of panel is 2 or less.
Loads are uniformly distributed over the panel.
Ratio of live to dead load is 3 or less.
Columns form an approximately rectangular grid (10 percent maximum
offset).
Successive spans in each direction do not differ by more than one-third of
the longer span.
When a panel is supported by beams on all sides, the relative stiffness of the
beams satisfies

1 2
l 2
0.2 5 (5.100)
2 l 1
where in direction of l 1
1
in direction of l 2
2
relative beam stiffness defined in the preceding equation
l span in the direction in which moments are being determined, c to c
1
of supports
l span perpendicular to l , c to c of supports
2
1
The basic equation used in direct design is the total static design moment in
a strip bounded laterally by the centerline of the panel on each side of the center-
line of the supports:
2
M o wl 2 l n (5.101)
8
where w uniform design load per unit of slab area and l clear span in
n
direction moments are being determined.
The strip, with width l , should be designed for bending moments for which
2
the sum in each span of the absolute values of the positive and average negative
moments equals or exceeds M .
o