Civil Engineering Reference
In-Depth Information
words, when the loads or spans or both become quite large, the slab thickness and column
sizes required for flat plates or flat slabs are of such magnitude that it is more economical
to use two-way slabs with beams, despite the higher formwork costs.
Another type of floor system is the
waffle slab
, an example of which is shown in the
accompanying photograph. The floor is constructed by arranging square fiberglass or
metal pans with tapered sides with spaces between them as shown in the photo. When the
concrete is placed over and between the pans, the waffle shape is obtained. The intervals
or gaps between the pans form the beam webs. These webs are rather deep and provide
large moment arms for the reinforcing bars. With waffle slabs, the weight of the concrete
is greatly reduced without significantly changing the moment resistance of the floor sys-
tem. As in flat plates, shear can be a problem near columns. Consequently, waffle floors
are usually made solid in those areas to increase shear resistance.
16.2
ANALYSIS OF TWO-WAY SLABS
Two-way slabs bend under load into dish-shaped surfaces, so there is bending in both
principal directions. As a result, they must be reinforced in both directions by layers of
bars that are perpendicular to each other. A theoretical elastic analysis for such slabs is a
very complex problem due to their highly indeterminate nature. Numerical techniques
such as finite difference and finite elements are required, but such methods are not really
practical for routine design.
Actually, the fact that a great deal of stress redistribution can occur in such slabs at
high loads makes it unnecessary to make designs based on theoretical analyses. Therefore
the design of two-way slabs is generally based on empirical moment coefficients, which,
though they might not accurately predict stress variations, result in slabs with satisfactory
overall safety factors. In other words, if too much reinforcing is placed in one part of a
slab and too little somewhere else, the resulting slab behavior will probably still be satis-
factory.
The total amount of reinforcement in a slab seems more important than its exact
placement.
You should clearly understand that though this chapter and the next are devoted to
two-way slab design based on approximate methods of analysis, there is no intent to pre-
vent the designer from using more exact methods. Designers may design slabs on the
basis of numerical solutions, yield-line analysis, or other theoretical methods, provided
that it can be clearly demonstrated that they have met all the necessary safety and service
ability criteria required by the ACI Code.
Although it has been the practice of designers for many years to use approximate
analyses for design and to use average moments rather than maximum ones, two-way
slabs so designed have proved to be very satisfactory under service loads. Furthermore,
they have been proved to have appreciable overload capacity.
16.3
DESIGN OF TWO-WAY SLABS BY THE ACI CODE
The ACI Code (13.5.1.1) specifies two methods for designing two-way slabs for gravity
loads. These are the direct design method and the equivalent frame method.
