Summer 2019

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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Page 52 of 55

ASPIRE Summer 2019 | 51 A A S H T O L R F D I n response to a question received by the ASPIRE® team, this article explains the technical background for the calculation of factored axial resistance. The factored axial resistance of concrete compressive components can be calculated using in Section of the 8th edition of the American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications. 1 To begin, Eq. indicates that the factored resistance P r can be calculated by multiplying the nominal axial capacity P n by the resistance factor φ: P r = φP n The resistance factor φ in this expression is based on the net tensile strain (see Fig. C5.5.4.2-1 in ref. 1). With that stated, the failure mode for the case of pure axial compression is compression-controlled; therefore, φ = 0.75. E q u a t i o n 5 . 6 . 4 . 4 - 2 a p p l i e s t o members with spiral reinforcement: P n = 0.85 k c ʹ f c A g − A st − A ps ( ) + f y A st − A ps f pe − E p ε cu ( ) ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ Equation applies to members with tie reinforcement: P n = 0.80 k c ʹ f c A g − A st − A ps ( ) + f y A st − A ps f pe − E p ε cu ( ) ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ A s e x p l a i n e d i n c o m m e n t a r y C5.6.4.4, the values of 0.85 and 0.80 that appear outside the brackets in Equations and 3, respectively, place upper limits on the usable resistance of compression members to account for unintended eccentricity. Historically, this was done by specifying a "minimum eccentricity" th at w as in th e ran ge of 5% to 10% of the column cross-sectional dimensions. However, the approach of specifying a minimum eccentricity has been abandoned in modern design codes including the AASHTO LRFD specifications. Placing a cap on the factored resistance diagram (P-M interaction curves) avoids the danger associated with producing designs in a region of the P-M interaction diagram where little bending resistance can be accommodated (Figure 1). In all other parts of the P-M interaction diagram, unintended eccentricities can be easily handled without creating a compliance problem with the specifications or a safety problem in the worst-case scenario. Prior to the 8th edition of the AASHTO LRFD specifications, the constant 0.85 appeared before f c ' in the above equations where the variable k c now appears. The origin of this k c factor dates back to research conducted at the University of Illinois Urbana- Champaign and Lehigh University, in which 564 normal-strength concrete columns were tested. The researchers concluded that there was a difference between the concrete compressive strength of the columns and that of t h e c o r r e s p o n d i n g c o n c r e t e t e s t cylinders. Most, if not all, failures observed in the reinforced concrete column specimens occurred in the top portions of the column specimens. As a result, the researchers attributed the 15% difference between the strength of the in-place concrete and the strength of concrete cylinders to potential segregation of concrete and migration of cement paste and air toward the top of the column, when concrete is consolidated by using internal vibrators. To make design provisions in the 8th edition of the AASHTO LRFD specifications applicable to a broader range of concrete compressive strengths, the factor k c replaces the constant 0.85 before f c ' as it appeared in the 7th edition. The k c term accounted f o r d e s i g n c o m p re s s i ve s t re n g t h s exceeding 10.0 ksi. Therefore, k c = 0.85 for f c ' ≤ 10 ksi; for f c ' > 10.0 ksi, k c is reduced at a rate of 0.02 for each 1.0 ksi of compressive strength in excess of 10.0 ksi to a minimum value of 0.75. Researchers found that reducing k c from 0.85 to 0.75 accounts for the cover spalling observed in tests of high- strength concrete columns. This cover spalling behavior was found to be influenced by the following: by Dr. Oguzhan Bayrak, University of Texas at Austin AASHTO LRFD Bridge Design Specifications: Factored Axial Resistance 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 P M Area to be avoided to account for unintended eccentricity Increased moment due to unintended eccentricity Figure 1. Upper limit on the usable resistance of compression members with tie reinforcement.

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