Structural Concrete - Hassoun

706 Chapter 18 Stairs
Figure 18.11
Case 1, ABC loaded.
Figure 18.12
Case 2, DBC loaded.
When the rise is absent, the stairs, ABC, act as a simply supported beam, and the maximum
bending moment occurs at midspan with value
M B = 1 4 PL = 1 2 PS
For a flight of stairs that consists of a number of runs and risers, the same approach can be
used; the bending moment diagram is shown in Fig. 18.15a. The moment in BB ′ is constant
and is equal to the moment at joint B,or2PS. Similarly, M C = M ′ C = 3PS, M D = M ′ D = 3PS,
and M E = M ′ E = 2PS.
If a landing is present at one or both ends, the load on the landing practically may be
represented by concentrated loads similar to the runs. The structural analysis may also be
performed by considering a load uniformly distributed on the flight of stairs. The moment
in every riser is constant and is obtained from the bending moment diagram of a simply
supported beam subjected to a uniform load (Fig. 18.15b). Example 18.3 illustrates the design
of a staircase using the two assumptions of concentrated loads and uniform loads.