Second-Order Stiffness Matrix and Loading Vector of a Beam-Column with Semirigid Connections on an Elastic Foundation
Publication: Journal of Engineering Mechanics
Volume 131, Issue 7
Abstract
The second-order stiffness matrix and corresponding loading vector of a prismatic beam–column subjected to a constant axial load and supported on a uniformly distributed elastic foundation (Winkler type) along its span with its ends connected to elastic supports are derived in a classical manner. The stiffness coefficients are expressed in terms of the ballast coefficient of the elastic foundation, applied axial load, support conditions, bending, and shear deformations. These individual parameters may be dropped when the appropriate effect is not considered; therefore, the proposed model captures all the different models of beams and beam–columns including those based on the theories of Bernoulli–Euler, Timoshenko, Rayleigh, and bending and shear.The expressions developed for the load vector are also general for any type or combinations of transverse loads including concentrated and partially nonuniform distributed loads. In addition, the transfer equations necessary to determine the transverse deflections, rotations, shear, and bending moments along the member are also developed and presented.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aristizabal-Ochoa, J. D. (1997). “First- and second-order stiffness matrix and load vector of beam–columns with semirigid connections.” J. Struct. Eng., 123(5), 669–678.
Aristizabal-Ochoa, J. D. (2001). “Stability and second-order analyses of frames with semirigid connections under uniformly distributed axial loads.” J. Struct. Eng., 127(11), 1306–1315.
Aristizábal-Ochoa, J. D. (2003). “Elastic stability and second-order analysis of 3D frames: Effects of column orientation.” J. Eng. Mech. 129(11), 1254–1267.
Aristizabal-Ochoa, J. D. (2004). “Column stability and minimum lateral bracing: Effects of shear deformations.” J. Eng. Mech., 130(10), 1223–1232.
Aydogan, M. (1995). “Stiffness-matrix formulation of beams with shear effect on elastic foundation.” J. Struct. Eng., 121(9), 1265–1270.
Chen, F. Y., and Pantelides, C. P. (1988). “Static Timoshenko beam–columns on elastic media.” J. Struct. Eng., 114(5), 1152–1172.
Hetenyi, M. (1967). Beams on elastic foundation, 8th Ed. Chap. VII, The University of Michigan, Ann Arbor, Mich.
Monforton, G. R., and Wu, T. S. (1963). “Matrix analysis of semi-rigidly connected frames.” J. Struct. Div. ASCE, 89(6), 13–42.
Scott, R. F. (1981). Foundation analysis, Prentice-Hall, Englewood Cliffs, N.J.
Timoshenko, S., and Gere, J. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
Information & Authors
Information
Published In
Copyright
© 2005 ASCE.
History
Received: Nov 4, 2003
Accepted: Oct 28, 2004
Published online: Jul 1, 2005
Published in print: Jul 2005
Notes
Note. Associate Editor: Hayder A. Rasheed
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.