The sectional shear design in B-regions of beams according to the empirically derived rules given in Ch. 11 of ACI 318-08 leads unavoidably to discrepancies when separately designing the adjacent D-regions by using a strut-and-tie model according to Appendix A of ACI 318-08. A “full member design” with the truss is the only model providing a consistent transition from B- to D-regions, in which the angle  of the inclined struts in the webs of beams can be derived from the rules given in Ch. 11 of ACI 318-08. Furthermore two important D-regions in beams are dealt with, which are the D-region where a point load is applied near the support and the D-region where a beam is indirectly supported by another beam. Finally a list of references is given for further guidance in application of strut-and-tie models or could serve as basis for writing such a document.

This example presents a strut-and-tie design for a storey-high propped cantilever beam that supports a single concentrated load near midspan and has a large rectangular opening between this point of loading and the fixed-ended support. The internal truss that is selected to carry the imposed loading to the supports is both externally and internally indeterminate. This creates a condition in which the calculated capacity of the STM designed region is affected by the relative stiffness of truss members and the degree of plasticity attributed to the truss. The design is investigated and validated by plastic and non-linear truss analyses, finite element analysis, and the results from a scale model test of the designed structure. This paper examines the influence of design and analysis assumptions on the performance of this structure under service and factored loads.

The load carrying capacity of the hinge region of an existing highway overpass is evaluated using the strut-and-tie modeling techniques of ACI 318-08 Appendix A. The overpass consists of a series of drop-in span girders supported at the center by doubly cantilevered pier girders. The hinge is achieved through the use of an incorporated steel piece, the so-called Cazaly hanger, in the ends of the span girders. This example examines the disturbed end regions of both the span girders and the pier girders. The strut-and-tie model demonstrates how the Cazaly hanger can be incorporated into the model. In addition, the girders are prestressed which is taken into account by modeling the prestressing as equivalent forces applied to the concrete. This example demonstrates how to evaluate the load carrying capacity of an existing concrete structure and how to develop a strut-and-tie model based on the existing reinforcement configuration.

A sectional approach is typically taken in US bridge engineering practice for the design of end regions in precast/prestressed I-Beams. However, these end regions are clearly discontinuity regions as there is a complex distribution of stresses created by reaction forces and the anchorage of prestressing strands. In accordance with ACI318-08, the design of these regions should satisfy the strut-and-tie provisions in Appendix A. There are several factors that make these apparently simple regions worthy of careful consideration in design. These include: (i) that the combination of shape and prestressing allow these members to be designed by sectional methods to resist very large shear forces that in turn leads to severe diagonal compressive stresses above supports, (ii) that longitudinal tie capacity at supports is most commonly provided by prestressing steel that is still within its calculated transfer length from the end of these members; (iii) that significant fanning action and changes in angle of diagonal compression occur throughout these end regions; and finally (iv) that these regions can often be the weak and brittle link in a very common class of members. This example presents how the strut-and-tie model provisions of ACI318-08 can be used to ensure the adequate design of end regions in large prestressed bulb-tee girders. Special attention is given to the influence of nodal zone dimensions and designer assumptions on the calculated capacity of these end regions.

A transfer girder with 18’-8” (5690 mm) span is designed to provide column-free space in a hotel conference room at the second floor. The girder is subject to a tributary area load from the third floor and a terminated column which is offset from the mid-span location. All analysis and design is completed in accordance with Appendix A of ACI 318-08. Preliminary designs are examined for two alternate truss models that differ primarily in the slope of the inclined web members. For the preferred option, a detailed design is completed including direct consideration of fan-shaped struts at the column locations. The detailed design is also compared against the reinforcement requirements from the sectional design provisions of ACI 318-08.