Analysis of Multiple‐Bay Frames Using Continuum Model
Publication: Journal of Structural Engineering
Volume 119, Issue 2
Abstract
An approximate method that can be used to determine displacements and member forces of multiple‐bay frames is presented. The method utilizes simple continuum models. Finite‐element representations of building frameworks resulting from continuum methodology require significantly fewer degrees of freedom than classical discrete finite‐element models, which individually model each of the beam and column elements. As a result, the use of continuum models to analyze structures can result in considerable savings in terms of computational effort. This makes the method attractive for use in the analysis of large frames, especially during the preliminary design stage. This paper reviews the continuum methodology and presents a method for computing discrete element forces from the continuum element displacements. In determining element forces, the effects of deep‐beam‐type cross‐sectional warping are approximated. Examples including the analysis of fixed‐ and pinned‐base single‐ and multiple‐bay plane frames illustrate the accuracy of the continuum analyses procedure.
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References
1.
Abdel‐Ghaffar, A. M. (1978). “Free lateral vibrations of suspension bridges.” J. Struct. Div., ASCE, 104(3), 503–525.
2.
Abdel‐Ghaffar, A. M. (1979). “Free torsional vibrations of suspension bridges.” J. Struct. Div., ASCE, 105(4), 767–788.
3.
Abdel‐Ghaffar, A. M. (1982). “Suspension bridge vibration: Continuum formulation.” J. Engr., Mech. Div., ASCE, 108(6), 1215–1231.
4.
Abrate, S., and Sun, C. T. (1983). “Dynamic analysis of geometrically nonlinear truss structures.” Computers and Struc., 17(4), 491–497.
5.
Chajes, M. J. (1990). “Nonlinear dynamic analysis of building frameworks using a continuum model,” Ph.D. thesis, University of California, Davis, Calif.
6.
Chajes, M. J., Romstad, K. M., and McCallen, D. B. (1990a). “Inelastic frame analysis using a continuum model.” Proc., 1990 Annual Tech. Session, Structural Stability Research Council, St. Louis, Mo., 109–120.
7.
Chajes, M. J., Romstad, K. M., and McCallen, D. B. (1990b). “Nonlinear frame analysis using a continuum model.” Proc., 8th Struct. Congress, ASCE, New York, N.Y.
8.
Chajes, J. J., Yang, C. Y., and Zhang, L. (1992). “Simplified seismic analysis of a 47‐story building.” Proc., 10th Stuct. Congress, ASCE, New York, N.Y., 448–451.
9.
Chitty, L. (1947). “On the cantilever composed of a number of parallel beams interconnected by cross bars.” Philosphical Mag., 38(285), 685–649.
10.
Engesser, F. (1907). Zum Einstürzder Brücke über den St. Lorenzstrom bei Quebec, Zentralblatt der Bauverwaltung, 93, 609 (in German).
11.
Flügge, W. (1962). Handbook of engineering mechanics. McGraw‐Hill, New York, N.Y.
12.
McCallen, D. B. (1986). “Continuum model for the nonlinear analysis of beam‐like lattice structures (UCRL‐53773),” Ph.D. thesis, Lawrence Livermore National Laboratory, Livermore, Calif.
13.
McCallen, D. B., and Romstad, K. M. (1987). “Application of a continuum model in building analysis.” Proc., Struct. Congress, ASCE, New York, N.Y., 344–358.
14.
McCallen, D. B., and Romstad, K. M. (1988). “A continuum model for the nonlinear analysis of beam‐like lattice structures.” Computers and Struc., 29(2), 177–197.
15.
McCallen, D. B., and Romstad, K. M. (1990). “A continuum model for lattice structures with geometric and material nonlinearities.” Computers and Struct., 37(5), 795–822.
16.
Necib, B., and Sun, C. T. (1989). “Analysis of beams using a higher order Timoshenko beam finite element.” J. Sound and Vibration, 130(1), 149–159.
17.
Noor, A. K. (1978a). “Thermal stress analysis of double‐layered grids.” J. Struct. Div., ASCE, 104(2), 251–262.
18.
Noor, A. K., Anderson, M. S., and Greene, W. H. (1978b). “Continuum models for beam and platelike lattice structures.” Am. Inst. of Aeronautics and Astronautics J., 16(12), 1219–1228.
19.
Noor, A. K., and Anderson. (1979). “Analysis of beam‐like lattice trusses.” Computer Methods in Appl. Mech. and Engrg., 20(1), 53–70.
20.
Noor, A. K., and Nemeth, M. P. (1980). “Micropolar beam models for lattice grids with rigid joints.” Computer Methods in Appl. Mech. and Engrg., 21(2), 249–263.
21.
Noor, A. K., and Weisstein, L. S. (1981). “Stability of beam‐like lattice trusses.” Computer Methods in Appl. Mech. and Engrg., 25(2), 179–193.
22.
Osterkamp, T. A. (1988). “Force calculations for a continuum model of lattice systems,” MS thesis, University of California at Davis, Davis, Calif.
23.
Sun, C. T., Kim, B. J., and Bogdanoff, J. L. (1981). “On the derivation of equivalent simple models for beam and plate‐like structures in dynamic analysis.” Proc., Dynamics Specialists Conf., American Institute of Aeronautics and Astronautics, New York, N.Y., 523–532.
24.
Sun, C. T., and Juang, J. N. (1986). “Modeling global structural damping in trusses using simple continuum models.” Am. Inst. of Aeronautics and Astronautics J., 24(1), 144–150.
25.
Timoshenko, S. (1943). “Suspension bridges.” J. Franklin Inst., 235(3), 213–238.
26.
Yang, T. Y. (1973). “Matrix displacement solution to elastica problems of beams and frames.” Int. J. Solids and Struct., 9(7), 829–842.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 119 • Issue 2 • February 1993
Pages: 522 - 546
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jan 31, 1992
Published online: Feb 1, 1993
Published in print: Feb 1993
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