Composite beam with integrated rupture initiator and aircraft fuselage including such beams. A composite beam (18) comprises a web (20) with a sinusoidal-shaped section and a bottom flange (22). The web (20) comprises a stack of at least one central layer of single-directional carbon fibers oriented along the depth of the beam, and aramide fiber and carbon fiber fabrics. The lower part of the beam (18) is designed so that rupture is initiated in it if the aircraft in which the beam is installed crashes. This is achieved by gluing the bottom flange (22) on the sides of the web (20), the bottom edge of each layer of single-directional carbon fibers is setback from the corresponding edges of the fabrics and saw-tooth cut-outs are formed in this bottom edge