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Thursday, September 30, 2010

what are B and D regions?

      B-Regions are parts of a structure in which Bernoulli's hypothesis of straight-line strain profiles applies. D-Regions, on the other hand, are parts of a structure with a complex variation in strain. D-Regions include portions near abrupt changes in geometry (geometrical discontinuities) or concentrated forces (statical discontinuities). Based on St. Venant's principle, the extent of a D-Region spans about one section depth of the region on either side of the discontinuity.
Figure 1 and Figure 2 show examples of the division between B-Regions and D-Regions in building and bridge structures, respectively. In the figures, the unshaded area with a notation B indicates B-Region, and the shaded area with a notation D is used to indicate D-Region. The notations h1, h2, h3, ... are used to denote the depth of structural members. The notations b1 and b2 denote the flange width of structural members.
Figure 1   Example of D-Regions in a Common Building Structure
(Click here to view a larger image)
Figure 2   Example of D-Regions in a Common Bridge Structure
(Click here to view a larger image)
    Most design practices for B-Regions are based on a model for behavior. As examples, design for flexure is based on conventional beam theory while the design for shear is based on the well-known parallel chord truss analogy. By contrast, the most familiar types of D-Regions, such as deep beams, corbels, beam-column joints, and pile caps, are currently still designed by empirical approaches or by using common detailing practices. For most other types of D-Regions, code provisions provide little guidance to designers. The Strut-and-Tie Method (STM)  is emerging as a code-worthy methodology for the design of all types of D-Regions in structural concrete.
     It is worth noting that although the STM is equally applicable to both B- and D-Region problems, it is not practical to apply the method to B-Region problems. The conventional beam theory for flexure and parallel chord truss analogy for shear are recommended for those designs.