ASPIRE is a quarterly magazine published by PCI in cooperation with the associations of the National Concrete Bridge Council. The editorial content focuses on the latest technology and key issues in the Concrete Bridge Industry.

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F H WA 46 | ASPIRE Winter 2018 St r u t - a n d - t i e m o d e l i n g ( S T M ) i s a technique that is commonly used to reduce complex states of stress in reinforced and p r e s t r e s s e d c o n c r e t e s t r u c t u r e s i n t o a simplified truss model. STMs are made up of elements loaded uniaxially in tension (referred to as ties) or compression (referred to as struts). The intersection points of the struts and ties are called nodes. This simplified truss model can then be analyzed using basic statics such as the method of sections or joints. The STM method is based on the lower-bound (that is, conservative) theorem of plasticity, which ensures a safe str ucture. Another unique aspect of STM analysis with respect to traditional sectional analysis is that it has a unified approach that considers all force effects (moment, shear, axial) simultaneously. Figures 1 and 2 show a concrete element with a complex stress profile and how STM can simplify these stresses into a truss model, respectively. When to Use STM? The American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications classify regions within structural concrete elements into two distinct categories: B-regions or D-regions. B-regions (beam or Bernouli) are regions within the element that have linear strain profiles, to which the principles of linear-elastic beam theory apply and for which traditional sectional design is appropriate. D-regions (disturbed or discontinuity), are regions that include concentrated loads or geometric discontinuities with strain profiles that are complex and nonlinear and therefore not appropriate for traditional sectional design. D-regions require analysis methods that can address these nonlinear strain profiles. Analysis using STM can address the stress complexities in a D-regions with a representative internal truss model that replicates the region's internal load transfer. Figure 3 is an example of a concrete member's B- and D-regions. The AASHTO LRFD specifications include guidance on determining the extent of each region. For the element shown in Fig. 3, only the D-regions require an analysis, such as STM, that can address their nonlinear strain profiles. Why Use STM? STM provides designers with an easy-to-use analysis tool for D-regions that would otherwise require a more complex analysis, such as finite element analysis. Improperly designed D-region can result in in-service cracking issues. The AASHTO LRFD specifications have design limits and detailing requirements to limit problematic D-region cracking. It should be noted that using sectional design for D-regions can lead to structural elements that are substantially underdesigned. A s e c o n d a r y b e n e f i t o f S T M i s t h a t it requires the designer to visualize and understand the internal load paths and stress fields, which, in turn, along with the STM design provisions, promote good overall element sizing and reinforcement detailing. How to Learn More? One of the most significant hurdles in using the STM technique is the lack of available guidance for bridge practitioners and, more specifically, guidance that follows the provisions i n t h e A A S H TO L R F D s p e c i f i c a t i o n s . Furthermore, very few U.S. colleges include S T M i n t h e i r s t r u c t u r a l e n g i n e e r i n g Strut-and-Tie Modeling: What, When, Why, and How by Reggie Holt, Federal Highway Administration Figure 1. Complex stress trajectories within concrete element. Note: dashed lines = compression; solid lines = tension. All Figures: Federal Highway Administration. Figure 2. Strut-and-tie model. Note: dashed lines = compression; solid lines = tension. Figure 3. B- and D-regions of an example concrete beam.

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