Second-order slope–deflection equations for imperfect beam–column structures with semi-rigid connections
A new set of second-order slope–deflection equations for Euler–Bernoulli beam–columns of symmetric cross-section including the effects of initial imperfections (i.e., initial curvature, out-of-plumbness and axial load eccentricities) and semi-rigid connections is developed in a classical manner. The...
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Published in | Engineering structures Vol. 32; no. 8; pp. 2440 - 2454 |
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Format | Journal Article |
Language | English |
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Elsevier Ltd
01.08.2010
Elsevier |
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ISSN | 0141-0296 1873-7323 |
DOI | 10.1016/j.engstruct.2010.04.018 |
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Abstract | A new set of second-order slope–deflection equations for Euler–Bernoulli beam–columns of symmetric cross-section including the effects of initial imperfections (i.e., initial curvature, out-of-plumbness and axial load eccentricities) and semi-rigid connections is developed in a classical manner. The proposed method has the following advantages: (1) it can be utilized in the stability and second-order analysis of framed structures made of Euler–Bernoulli imperfect beam–columns with rigid, semi-rigid, and simple connections subject to axial and transverse loads; (2) the effects of semi-rigid connections and member imperfections are condensed into the slope–deflection equations for tension and compression axial loads; (3) it is more accurate than any other method available in the technical literature and capable of capturing not only the first-order and second-order elastic responses of frames made of imperfect beam–columns but also the phenomenon of reversals of deflections along the members as the axial loads are increased; and (4) it is powerful, practical, versatile and easy to apply. Analytical studies indicate that the initial imperfections (a) act as if they were additional transverse loads proportional to the bending stiffness and magnitudes of the imperfections of the corresponding beam–column; and (b) are detrimental to structures, increasing the lateral deflections, moments, and shears, and also reducing the critical axial loads of beam–columns and framed structures. This is particularly critical in structures made of beam–columns with initial crookedness and low stiffness connections subjected to high compressive axial loads. In addition, the effects of initial curvature are amplified by the compressive axial loads applied at the ends of the member. Four comprehensive examples are included that show the effectiveness of the proposed method. |
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AbstractList | A new set of second-order slope–deflection equations for Euler–Bernoulli beam–columns of symmetric cross-section including the effects of initial imperfections (i.e., initial curvature, out-of-plumbness and axial load eccentricities) and semi-rigid connections is developed in a classical manner. The proposed method has the following advantages: (1) it can be utilized in the stability and second-order analysis of framed structures made of Euler–Bernoulli imperfect beam–columns with rigid, semi-rigid, and simple connections subject to axial and transverse loads; (2) the effects of semi-rigid connections and member imperfections are condensed into the slope–deflection equations for tension and compression axial loads; (3) it is more accurate than any other method available in the technical literature and capable of capturing not only the first-order and second-order elastic responses of frames made of imperfect beam–columns but also the phenomenon of reversals of deflections along the members as the axial loads are increased; and (4) it is powerful, practical, versatile and easy to apply. Analytical studies indicate that the initial imperfections (a) act as if they were additional transverse loads proportional to the bending stiffness and magnitudes of the imperfections of the corresponding beam–column; and (b) are detrimental to structures, increasing the lateral deflections, moments, and shears, and also reducing the critical axial loads of beam–columns and framed structures. This is particularly critical in structures made of beam–columns with initial crookedness and low stiffness connections subjected to high compressive axial loads. In addition, the effects of initial curvature are amplified by the compressive axial loads applied at the ends of the member. Four comprehensive examples are included that show the effectiveness of the proposed method. |
Author | Aristizabal-Ochoa, J. Darío |
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Cites_doi | 10.1061/(ASCE)0733-9445(1997)123:5(669) 10.1002/nme.1510 10.1016/j.engstruct.2008.02.007 10.1061/(ASCE)0733-9445(1997)123:6(799) 10.1016/j.engstruct.2006.07.012 |
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Keywords | Frames Large deflections Second-order analysis Stability Beams Beam–columns Imperfect columns Nonlinear analysis Initial imperfections Semi-rigid connections Structural analysis Structural design Second order Structural stability Connection Modeling Frame structure Beam-columns Example Defect Beam column structure |
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References | Samuelsson, Zienkiewicz (b7) 2006; 67 Salmon, Johnson (b9) 1996 Wilson, Maney (b6) 1915; 80 Aristizabal-Ochoa (b2) 1997; 123 Aristizabal-Ochoa (b4) 2008; 30 Norris, Wilbur (b8) 1960 Aristizabal-Ochoa (b1) 1997; 123 Timoshenko, Gere (b5) 1961 Aristizabal-Ochoa (b3) 2007; 29 Salmon (10.1016/j.engstruct.2010.04.018_b9) 1996 Timoshenko (10.1016/j.engstruct.2010.04.018_b5) 1961 Aristizabal-Ochoa (10.1016/j.engstruct.2010.04.018_b1) 1997; 123 Aristizabal-Ochoa (10.1016/j.engstruct.2010.04.018_b2) 1997; 123 Norris (10.1016/j.engstruct.2010.04.018_b8) 1960 Aristizabal-Ochoa (10.1016/j.engstruct.2010.04.018_b3) 2007; 29 Wilson (10.1016/j.engstruct.2010.04.018_b6) 1915; 80 Aristizabal-Ochoa (10.1016/j.engstruct.2010.04.018_b4) 2008; 30 Samuelsson (10.1016/j.engstruct.2010.04.018_b7) 2006; 67 |
References_xml | – volume: 80 year: 1915 ident: b6 article-title: Slope-deflection method publication-title: Univ Illinois Eng Exp Station Bull – year: 1996 ident: b9 article-title: Steel structures: design and behavior – volume: 29 start-page: 991 year: 2007 end-page: 1003 ident: b3 article-title: Large deflection and postbuckling behavior of Timoshenko beam–columns with semi-rigid connections including shear and axial effects publication-title: J Eng Struct – year: 1960 ident: b8 article-title: Elementary structural analysis – volume: 30 start-page: 2517 year: 2008 end-page: 2527 ident: b4 article-title: Slope-deflection equations for stability and second-order analysis of Timoshenko beam–column structures with semi-rigid connections publication-title: J Eng Struct – volume: 123 start-page: 669 year: 1997 end-page: 678 ident: b1 article-title: First- and second-order stiffness matrices and load vector of beam–columns with semi-rigid connections publication-title: J Struct Engrg, ASCE – volume: 123 start-page: 799 year: 1997 end-page: 807 ident: b2 article-title: Story stability of braced, partially braced, and unbraced frames: classical approach publication-title: J Struct Engrg, ASCE – year: 1961 ident: b5 article-title: Theory of elastic stability – volume: 67 start-page: 149 year: 2006 end-page: 157 ident: b7 article-title: History of the stiffness method publication-title: Internat J Numer Methods Engrg – volume: 80 year: 1915 ident: 10.1016/j.engstruct.2010.04.018_b6 article-title: Slope-deflection method publication-title: Univ Illinois Eng Exp Station Bull – volume: 123 start-page: 669 issue: 5 year: 1997 ident: 10.1016/j.engstruct.2010.04.018_b1 article-title: First- and second-order stiffness matrices and load vector of beam–columns with semi-rigid connections publication-title: J Struct Engrg, ASCE doi: 10.1061/(ASCE)0733-9445(1997)123:5(669) – volume: 67 start-page: 149 year: 2006 ident: 10.1016/j.engstruct.2010.04.018_b7 article-title: History of the stiffness method publication-title: Internat J Numer Methods Engrg doi: 10.1002/nme.1510 – year: 1960 ident: 10.1016/j.engstruct.2010.04.018_b8 – year: 1996 ident: 10.1016/j.engstruct.2010.04.018_b9 – volume: 30 start-page: 2517 issue: 9 year: 2008 ident: 10.1016/j.engstruct.2010.04.018_b4 article-title: Slope-deflection equations for stability and second-order analysis of Timoshenko beam–column structures with semi-rigid connections publication-title: J Eng Struct doi: 10.1016/j.engstruct.2008.02.007 – year: 1961 ident: 10.1016/j.engstruct.2010.04.018_b5 – volume: 123 start-page: 799 issue: 6 year: 1997 ident: 10.1016/j.engstruct.2010.04.018_b2 article-title: Story stability of braced, partially braced, and unbraced frames: classical approach publication-title: J Struct Engrg, ASCE doi: 10.1061/(ASCE)0733-9445(1997)123:6(799) – volume: 29 start-page: 991 issue: 6 year: 2007 ident: 10.1016/j.engstruct.2010.04.018_b3 article-title: Large deflection and postbuckling behavior of Timoshenko beam–columns with semi-rigid connections including shear and axial effects publication-title: J Eng Struct doi: 10.1016/j.engstruct.2006.07.012 |
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SubjectTerms | Applied sciences Beams Beam–columns Buildings Buildings. Public works Computation methods. Tables. Charts Exact sciences and technology External envelopes Frames Imperfect columns Initial imperfections Joints Large deflections Nonlinear analysis Second-order analysis Semi-rigid connections Stability Structural analysis Structural analysis. Stresses |
Title | Second-order slope–deflection equations for imperfect beam–column structures with semi-rigid connections |
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