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Unformatted text preview: Lecture 22  Biaxial Columns Lecture 22  Biaxial Columns Design Design July 30, 2003 CVEN 444 Lecture Goals Lecture Goals Short Column Biaxial Design Slender Column Design Biaxial Bending and Axial Biaxial Bending and Axial Load Load Ref. PCA Notes on ACI 31895 Unaxial bending about yaxis Biaxial Bending and Axial Biaxial Bending and Axial Load Load Ref. PCA Notes on ACI 31895 The biaxial bending moments M x = P*e y M y = P*e x Approximate Analysis Approximate Analysis Methods Methods Use Reciprocal Failure surface S 2 (1/P n ,e x ,e y ) The ordinate 1/P n on the surface S 2 is approximated by ordinate 1/P n on the plane S’ 2 (1/P n e x ,e y ) Plane S 2 is defined by points A,B, and C. Approximate Analysis Approximate Analysis Methods Methods P = Axial Load Strength under pure axial compression (corresponds to point C ) M nx = M ny = 0 P 0x = Axial Load Strength under uniaxial eccentricity, e y (corresponds to point B ) M nx = P n e y P 0y = Axial Load Strength under uniaxial eccentricity, e x (corresponds to point A ) M ny = P n e x Approximate Analysis Approximate Analysis Methods Methods Design: P u M uy , M ux P u , P u e x , P u e y Approximate Analysis Approximate Analysis Methods Methods P n = Nominal axial load strength at eccentricities, e x & e y Limited to cases when 0y 0x n 0y 0x n n 1 1 1 1 1 1 1 1 1 P P P P P P P P P+ ≈ ⇒+ = ′ ≈ g c n 1 . A f P ≥ Biaxial Bending in Short Biaxial Bending in Short Columns Columns 1) Calculate P 2) Calculate P 0y ( P n for e = e x , e y = 0 ) 3)Calculate P 0x ( P n for e x = 0, e = e y ) 4) Calculate P n (from Bresler’s Formula ) Analysis Procedure: Reciprocal Load Method Bresler’s Formula: Steps: 0y 0x n 1 1 1 1 P P P P+ 2245 Biaxial Bending in Short Biaxial Bending in Short Columns Columns where, φ = 0 .6 5 n u P P φ ≤ Biaxial Column Example Biaxial Column Example The section of a short tied column is 16 x 24 in. and is reinforced with 8 #10 bars as shown. Determine the allowable ultimate load on the section φ P n if its acts at e x = 8 in. and e y = 12 in. Use f c = 5 ksi and f y = 60 ksi. Biaxial Column Example Biaxial Column Example Compute the P load, compression with no moments ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 st c g st st y 2 2 n0 8 1.27 in 10.16 in 0.85 0.85 5 ksi 24.0 in. 24.0 in. 10.16 in 10.16 in 60 ksi 2198.4 k 0.8 2198.4 k 1758.7 k A P f A A A f P rP = = =+ =+ = = = = Biaxial Column Example Biaxial Column Example Compute P nx , by starting with e y term and assume that compression controls. Check by Compute the nominal load, P nx and assume second compression steel does not contribute assume small ( 29 y 2 2 12 in. 21.5 in. 14.33 in....
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This note was uploaded on 10/03/2011 for the course CVEN 444 taught by Professor Staff during the Summer '08 term at Texas A&M.
 Summer '08
 Staff

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