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.
Issue link: http://www.aspiremagazinebyengineers.com/i/697527
A A S H T O L R F D 52 | ASPIRE Summer 2016 B eam regions (B-regions), where it is appropriate to assume that plane sections remain plane after loading, may be designed for shear and torsion using either the sectional modified compression-field theor y (MCFT) resistance model or the strut-and-tie method (STM). Disturbed regions (D-regions) where the plane-sections-remain-plane assumption of flexural theory is not valid should be designed for shear and torsion using the STM. B-region theory assumes that the resistance at a par ticular section depends only on the calculated values of the sectional force effects—that is, moment, shear, axial load, and torsion—and does not consider the specific details of how the force effects are introduced into the member. The STM recognizes the significance of how the loads are introduced into a D-region and how that region is supported. It is applicable to both B- and D-regions, but it is not practical to apply the STM to B-regions. As the STM used for D-regions proportions and details members without an explicit treatment of moment, shear, torsion or thrust, it will not be discussed further herein. (See my column in the Winter 2011 issue of ASPIRE ™ .) Sections that are designed for live loads using the distribution-factor methods for beam-slab bridges are not typically investigated for torsion. To r s i o n i s o f t e n c a t e g o r i z e d a s e i t h e r c o m p a t i b i l i t y o r e q u i l i b r i u m t o r s i o n a s illustrated in Table 1. Equilibrium torsion is required for stable equilibrium by the topology of the structure and must be addressed in the design. All torsion in a statically determinant structure is equilibrium torsion. Torsion in a statically indeterminate structure may be either compatibility or equilibrium torsion. Torsion that results from rotational restraint, but which is not required to keep the applied loads in stable equilibrium because other load paths exist to support the loads, is called compatibility torsion. It is not necessary to design for compatibility torsion as long as the other load paths are properly designed for the redistributed forces. Consideration should be given to aesthetic issues that arise from cracking associated with not designing for compatibility torsion. Thus, in a statically indeterminate structure where significant reduction of torsional moment in a member can occur due to redistribution of internal forces upon cracking, the applied factored torsional moment at a section T u may be reduced to ϕ T cr provided that moments and forces in the member and adjoining members are adjusted to account for the redistribution. If the factored torsional moment T u is less than or equal to 25% of the factored pure torsional cracking moment, only a very small reduction in shear capacity or flexural capacity will occur and, hence, can be neglected. Further, equations for the torsional cracking moment for solid and hollow sections are specified. The nominal torsional resistance is taken as: s T n = 2 A 0 A t f y cot θ with the familiar variables used for shear resistance with the addition of A 0 , the area enclosed by the shear-flow path. The topic of combined shear and torsion will be discussed in a future column. by Dr. Dennis R. Mertz The AASHTO LRFD Bridge Design Specifications: Torsional Resistance Table 1. Categorization of torsion. Note: N/A = not applicable. Figure: Dennis Mertz. Structural Determinacy Torsion Category Equilibrium Compatibility Statically Determinate F N/A Statically Indeterminate F F