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 inEngineering structures Vol. 32; no. 8; pp. 2440 - 2454
Main Author Aristizabal-Ochoa, J. Darío
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.08.2010
Elsevier
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ISSN0141-0296
1873-7323
DOI10.1016/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.
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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Issue 8
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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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
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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
URI https://dx.doi.org/10.1016/j.engstruct.2010.04.018
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