THE CONCRETE BRIDGE MAGAZINE

WINTER 2013

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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EdiTor's NoTE If you would like to have a specific provision of the AASHTO LRFD Bridge Design Specifications explained in this series of articles, please contact us a www .aspirebridge.org. 48 | ASPIRE , Winter 2013 A A S H T O L R F D T h e A A S H T O L R F D B r i d g e D e s i g n Specifications currently includes the following six different procedures to estimate the shear resistance of concrete members:. a. Article 5.8.3.4.1—Simplified Procedure for Nonprestressed Sections b. Article 5.8.3.4.2—General Procedure c. Article 5.8.3.4.2 reference to Appendix B 5 — G e n e r a l P r o c e d u r e fo r S h e a r Design with Tables d. A r t i c l e 5 . 8 . 3 . 4 . 3 — S i m p l i f i e d P r o c e d u r e f o r P r e s t r e s s e d a n d Nonprestressed Sections e. Article 5.8.6—Shear and Torsion for Segmental Box Girder Bridges f. Article 5.6.3—Strut-and-Tie Model Procedures a through d are based upon the sectional design model. Procedure e is only applicable to segmental concrete box girders. P r o c e d u r e f d o e s n o t u s e t h e s e c t i o n a l method. S e c t i o n a l m o d e l s a r e b a s e d u p o n t h e assumption that the reinforcement required at a particular section depends only on the s e p a r a t e d v a l u e s o f t h e fa c t o r e d s e c t i o n force effects (moment, axial load, shear, and torsion) and does not consider the specific details of how the force effects are introduced into the member. Sectional models assume t h a t s h e a r d i s t r i b u t i o n r e m a i n s u n i fo r m and that the plane sections remain plane a f t e r l o a d i n g . T h i s a s s u m p t i o n i s t r u e where the conventional methods of strength of materials are applica ble. The sectional model is appropriate for the design of typical b r i d g e g i r d e r s , s l a b s , a n d o t h e r r e g i o n s of component s wher e the assumptions of t r a d i t i o n a l e n g i n e e r i n g b e a m t h e o r y a r e v a l i d . N e a r s u p p o r t s , n e a r t h e p o i n t s o f application of concentrated loads, at abrupt changes in cross section, and for deep beams where the distance between the centers of applied load and the suppor ting reactions is less than about twice the member depth, sectional models are not appropriate and the strut-and-tie model must be used. O n l y P r o c e d u r e s a , c , a n d f o f t h e s i x c u r r e n t p r o c e d u r e s l i s t e d p r e v i o u s l y f o r estimating shear resistance were included in the first edition of the LRFD Specifications published in 1994. At that time, the basic s e c t i o n a l m o d e l o f A r t i c l e 5 . 8 . 3 . 4 . 2 wa s t h e p r o c e d u r e t h a t i s n o w A p p e n d i x B 5 ( P r o c e d u r e c ) . I t i s b a s e d u p o n t h e modified compression field theor y (MCFT), w h i c h i s a c o m p r e h e n s i v e b e h a v i o r a l m o d e l f o r t h e r e s p o n s e o f d i a g o n a l l y cracked concrete subject to in-plane shear and normal stresses. The shear resistance i n t h e M C F T m o d e l i s a f u n c t i o n o f t h e calculated longitudinal strain at the mid- depth of the member, ɛ x , the shear stress, v u , and the concrete compressive strength, f c ′ . Shear design was iterative and required e n t e r i n g t h e s e v a l u e s i n t o t h e t a b l e s fo r the determination of β, a factor indicating a b i l i t y o f d i a g o n a l l y c r a c k e d c o n c r e t e to transmit tension and shear and θ , the angle of inclination of diagonal compressive stresses. These two variables were then used in the calculation of shear resistance. A s i m p l i f i c a t i o n o f t h i s g e n e r a l M C F T p r o c e d u r e wa s a l s o i n c l u d e d i n t h e f i r s t edition (Procedure a). This simplification for certain nonprestressed sections specifies that β be taken as 2.0 and θ as 45 degrees r e s u l t i n g i n s h e a r r e s i s t a n c e s e s s e n t i a l l y identical to those traditionally used for these sections. Finally, the strut-and-tie model (Procedure f) was introduced in the first edition as a third procedure to estimate shear resistance where the sectional models are not appropriate. O v e r t h e y e a r s , t h e n u m b e r o f s h e a r- resistance procedures has grown as bridge engineers and owners reacted to the newness of the MCFT and the strut-and-tie models, and the complication of the iterative nature of the MCFT as presented in the first edition o f t h e LRFD Specifications . I n t h e n e x t article, I will explore what the three added shear-resistance procedures (Procedures b, d, and e) represent and why they are in the LRFD Specifications. by Dr. Dennis R. Mertz AAsHTo LrFd: shear resistance, Part 1 Six Procedures to Estimate Shear Resistance • Article 5.8.3.4.1—Simplified Procedure for Nonprestressed Sections • Article 5.8.3.4.2—General Procedure • Article 5.8.3.4.2 reference to Appendix B5—General Procedure for Shear Design with Tables • Article 5.8.3.4.3—Simplified Procedure for Prestressed and Nonprestressed Sections • Article 5.8.6—Shear and Torsion for Segmental Box Girder Bridges • Article 5.6.3—Strut-and-Tie Model AspireBook_Win13.indb 48 12/28/12 11:40 AM

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