Structural Concrete - Hassoun

556 Chapter 16 Continuous Beams and Frames
Figure 16.1 Slab loads on supporting beams: (a) one-way direction, L/s > 2, and
(b) two-way direction, L/s ≤ 2.
16.2 MAXIMUM MOMENTS IN CONTINUOUS BEAMS
16.2.1 Basic Analysis
The computation of bending moments and shear forces in reinforced concrete continuous beams
is generally based on the elastic theory. When reinforced concrete sections are designed using the
strength design method, the results are not entirely consistent with the elastic analysis. However,
the ACI Code does not include provisions for a plastic design or limit design of reinforced concrete
continuous structures except in allowing moment redistribution, as is explained later in this
chapter.
16.2.2 Loading Application
The bending moment at any point in a continuous beam depends not only on the position of loads
on the same span but also on the loads on the other spans. In the case of dead loads, all spans must
be loaded simultaneously because the dead load is fixed in position and magnitude. In the case of
moving loads or occasional live loads, the pattern of loading must be considered to determine the
maximum moments at the critical sections. Influence lines may be used to determine the position
of the live load to calculate the maximum and minimum moments. However, in this chapter, simple
rules based on load–deflection curves are used to determine the loading pattern that produces
maximum moments.
16.2.3 Maximum and Minimum Positive Moments within a Span
The maximum positive bending moment in a simply supported beam subjected to a uniform
load w K/ft is at midspan, and M = wl 2 /8. If one or both ends are continuous, the restraint at the
continuous end will produce a negative moment at the support and slightly shift the location of