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/306162
52 | ASPIRE , Winter 2011 A A S H T O L R F D by Dr. Dennis R. Mertz T he strut-and-tie model of Article 5.6.3 of the AASHTO LrFD Bridge Design S p e c i f i c a t i o n s p r o v i d e s a n a l t e r n a t e t o traditional models for proportioning reinforcing steel within structural concrete components at strength and extreme event limit states. Traditional sectional models are based on the assumption that the reinforcement required at a particular section depends only on the section force effects of moment, shear, and torsion. These sectional models do not consider the interaction between these force effects. For control of cracking u n d e r s e r v i c e l o a d s , t h e magnitude of principal tensile stresses can be checked using the principles of Mohr's Circle. A c c o r d i n g t o t h e L r F D Specifications, the strut-and- tie model may be applied to proportioning reinforcement in any component or parts of a component, but must be applied where nonlinear s t r a i n d i s t r i b u t i o n s e x i s t . Such nonlinear distributions typically exist in deep pile caps and pier caps and, in general, anywhere applied loads or support reactions are less than two member depths apart. In such circumstances, linear strain distributions cannot develop. In the application of the strut-and-tie model, rather than determine force effects at individual sections along the component, load paths carr ying the applied loads t o t h e s u p p o r t r e a c t i o n s a r e v i s u a l i z e d w i t h i n t h e component. These load paths are assumed to be straight lines that form a truss within the component. At the limit after significant cracking, the initially curved compressive-stress trajectories do indeed become straight lines, called struts. The straight tension load paths, called ties, represent the steel reinforcement, either prestressed or nonprestressed. Many different load paths and thus strut-and- tie models are viable for a particular component, just as many solutions exist to any design problem. The more inefficient visualized load paths will require more reinforcement. The most efficient load paths are relatively self evident. A simple, classical strut-and-tie model of a deep beam is shown in Figure C184.108.40.206-1 of the LRFD Specifications. In the case of the beam shown in the figure, each of the applied loads and nearest support reactions are less than two member depths apart. Many example strut- and-tie models representing more realistic bridge components are included in the final r epor t for National Cooperativ e Highway Research Program (NCHRP) Project 20-7, Task 217, Verification and Implementation of Strut-and-Tie Model in LrFD Bridge Design Specifications by Modjeski & Masters. This valuable resource is available for free download at the Transpor tation Research Board website, http://apps.trb.org/cmsfeed/ TRBNetProjectDisplay.asp?ProjectID=1232. Design examples are also given in the Portland Cement Association publication EB231 titled AASHTO LrFD Strut-and-Tie Model Design Examples. After the load paths of the applied loads to the support reactions are visualized in the model, the actual load paths must be realized in the component. The size of the compression strut defined in LRFD Article 220.127.116.11.2 must be of sufficient cross-sectional area to carry the compression force without exceeding the limiting compressive stress of LRFD Article 18.104.22.168.3. Steel reinforcement must be provided within the tension ties to carry tension force when the steel is at yield. Further, the steel must be sufficiently anchored to carry the tie force along its entire length. The nodes at which the struts and ties meet must also s a t i s f y c o m p r e s s i o n - s t r e s s limits specified in LRFD Article 22.214.171.124. F i n a l l y, a n o r t h o g o n a l grid of reinforcement must be provided near the faces of the components to control the significant cracking expected at the limit when the struts and ties are realized. The strut-and-tie model is a powerful tool for strength load cases when conventional m e t h o d s o f s t r e n g t h o f materials are no longer valid. It harkens back to when the structural engineer first learns to analyze a simple truss. By visualizing the members of the truss, the struts and ties, the designer achieves a better understanding of the mechanisms that allow complex structures to safely carry loads. the strut-and-tie Model: Visualizing Load Paths Figure C126.96.36.199-1 from the AASHTO LRFD Bridge Design Specifications. Book_Win11.indb 52 1/4/11 2:34 PM