Bursting and Spalling in Pretensioned U-Beams - Ferguson ...

3.2.1.1 Linear and Nonlinear Stress DistributionsWithin the end region of a prestressed concrete beam, concentrated prestressingforces spread to the entire beam cross section. At some distance from the beam end, theinternal stresses become distributed linearly, there conforming to one of the basic tenetsof beam theory: the Bernoulli-Navier assumption that “plane sections remain plane.”Closer to the end, however, the state of stress is “disturbed” (i.e. nonlinear). Strut-and-tietheory (Schlaich, Schäfer & Jennewein, 1987) refers to regions with linear stressdistributions as B-regions, after Beam theory or in honor of Bernoulli; and regions withnonlinear stress distributions as D-regions, after the Disturbed state of stress.Strictly speaking, no hard line divides D-regions from B-regions. Elastic analysisof a post-tensioned beam (Figure 3.1) shows the gradual transition to a linear stressdistribution. In this figure, the stress distribution is linear where the stress trajectories areparallel, or about a distance h from the end of the beam as predicted by Saint-Vénant’sprinciple.hhFigure 3.1 Elastic stress trajectories in a post-tensioned concrete beam, illustratingthe division into D- and B-regions (after Schlaich, Schäfer & Jennewein, 1987)98