Flexural‐Torsional Buckling of Monosymmetric Arches
Publication: Journal of Structural Engineering
Volume 113, Issue 10
Abstract
A flexural‐torsional buckling theory is developed for arches of monosymmetric cross section. Nonlinear strain‐displacement relations are derived for the axial and shear strains, and these are substituted into the second variation of the total potential to obtain the buckling equation. Closed form solutions are obtained for arches subjected to equal and opposite end moments and for arches and rings subjected to a uniformly distributed radial load. The solutions are compared with previous theoretical results.
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References
1.
Anderson, J. M., and Trahair, N. S. (1972). “Stability of monosymmetric beams and cantilevers.” Struct. Div., ASCE, 98(1), 269–286.
2.
Barsoum, R. S., and Gallagher, R. H. (1970). “Finite element analysis of torsional and torsional‐flexural stability problems.” Int. J. Numer. Methods in Egnrg., 2(3), 335–352.
3.
Bazant, Z. P., and El Nimeiri, M. (1973). “Large‐deflection spatial buckling of thin‐walled beams and frames.” J. Engrg. Mech. Div., ASCE, 99(6), 1259–1281.
4.
Bleich, F. (1952). Buckling strength of metal structures, McGraw‐Hill, New York, N.Y.
5.
Cheney, J. A. (1963). “Bending and buckling of thin‐walled open‐section rings.” J. Engrg. Mech. Div., ASCE, 89(5), 17–44.
6.
Cuk, P. E. (1984). “Flexural‐torsional buckling in frame structures,” thesis presented to the University of Sydney, at Sydney, N.S.W., Australia, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
7.
Goldberg, J. E., and Bogdanoff, J. L. (1962). “Out‐of‐plane buckling of I‐section rings.” Publications, Int. Assoc., for Bridge and Struct. Engrg., 22, 73–92.
8.
Goodier, J. N. (1942). “Flexural‐torsional buckling of bars of open section, under bending, eccentric thrust, or torsional loads.” Bulletin 28, Cornell Univ. Engrg. Experimental Station, Ithaca, N.Y.
9.
Hancock, G. J., and Trahair, N. S. (1978). “Finite element analysis of the lateral buckling of continuously restrained beam‐columns.” Civ. Engrg. Trans., Instn. of Engrs., Australia, CE20(2), 120–127.
10.
Hasegawa, A., Lujanage, K., Ikeda, T., and Nishino, F. (1985). “A concise and explicit formulation of out‐of‐plane instability of thin‐walled members.” Struct. Engrg./Earthquake Engrg., Japan Soc. of Civ. Engrs., 2(1), 81–89.
11.
Hill, H. N. (1942). “The lateral instability of unsymmetrical I‐sections.” J. Aeronaut. Sci., 9(5), 175–180.
12.
Kerensky, O. A., Flint, A. R., and Brown, W. C. (1956). “The basis for design of beams and plate girders in the revised British standard 153.” Proc. Inst. of Civ. Engrs., London, England, 5, III(2), 396–486.
13.
Kitipomchai, S., and Dux, P. F. (1982). Discussion of “Wagner hypothesis in beam and column theory,” by Morris Ojalvo.J. Engrs. Mech. Div., ASCE, 108(3), 570–572.
14.
Kitipomchai, S., and Trahair, N. S. (1975). “Elastic behaviour of tapered monosymmetric I‐beams.” J. Struct. Div., ASCE, 101(8), 1661–1678.
15.
Kitipomchai, S., Wang, C. M., and Trahair, N. S. (1986). “Buckling of monosymmetric I‐beams under moment gradient.” J. Struct. Engrg., ASCE, 112(4), 781–799.
16.
Kitipomchai, S., Wang, C. M., and Trahair, N. S. (1987). Closure to discussion by Ojalvo on “Buckling of Monosymmetric I‐Beams Under Moment Gradient.” J. Struct. Engrs., ASCE, 113(6), 1391–1395.
17.
Langhaar, H. L. (1962). Energy methods in applied mechanics. John Wiley & Sons, Inc., New York, N.Y.
18.
O'Connor, C. (1964). “The buckling of a monosymmetric beam loaded in the plane of symmetry.” Australian J. of Appl. Sci., 15(4), 191–203.
19.
Ojalvo, M. (1981). “Wagner hypothesis in beam and column theory.” J. Engrg. Mech. Div., ASCE, 107(4), 669–677.
20.
Ojalvo, M. (1987). Discussion of “Buckling of monosymmetric I‐beams under moment gradient,” by S. Kitipomchai, C. M. Wang and N. S. Trahair, J. Struct. Engrg., ASCE, 113(6), 1387–1391.
21.
Ojalvo, M., Demuts, E., and Tokarz, F. J. (1969). “Out‐of‐plane buckling of curved members.” J. Struct. Div., ASCE, 95(10), 2305–2316.
22.
Papangelis, J. P., and Trahair, N. S. (1986). “In‐plane finite element analysis of arches.” Proc. Pacific Struct. Steel Conf., Auckland, New Zealand, 4, 333–349.
23.
Papangelis, J. P., and Trahair, N. S. (1987a). “Flexural‐torsional buckling of arches.” J. Struct. Engrg., ASCE, 113(4), 889–906.
24.
Papangelis, J. P., and Trahair, N. S. (1987b). “Finite element analysis of arch lateral buckling.” Civ. Engrg. Trans., Inst. of Engrs., Australia, CE29(1), 34–39.
25.
Papangelis, J. P., and Trahair, N. S. (1987c). “Flexural‐torsional buckling tests on arches.” J. Struct. Engrg., ASCE, 113(7), 1433–1443.
26.
Papangelis, J. P., and Trahair, N. S. (1987d). “Building of monosymmetric arches under point loads.” Research Report, School of Civ. and Mining Engrg., Univ. of Sydney, Sydney, Australia.
27.
Pettersson, O. (1951). “Combined bending and torsion of I‐beams of monosymmetric cross‐section.” Bulletin No. 10, Div. of Building Statics and Struct. Engrg., Royal Inst. of Tech., Stockholm, Sweden.
28.
Roberts, T. M., and Burt, C. A. (1985). “Instability of monosymmetric I‐beams and cantilevers.” Int. J. Mech. Sci., 27(5), 313–324.
29.
Stussi, F. (1943–44), “Lateral buckling and vibration of arches.” Publications, Int. Assoc., for Bridge and Struct. Engrg., 7, 327–343.
30.
Teng, J. G., and Rotter, J. M. (1986). “On the out‐of‐plane buckling of monosymmetric rings.” Proc. 10th Australian Conf. Mech. of Struct., and Materials, Adelaide, Australia, 545–549.
31.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. 2nd ed., McGraw‐Hill, New York, N. Y.
32.
Tokarz, F. J. (1968). “Lateral torsional buckling of arches,” thesis presented to Ohio State University, at Columbus, Ohio, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
33.
Tokarz, F. J. (1971). “Experimental study of lateral buckling of arches.” J. Struct. Div., ASCE, 97(2), 545–559.
34.
Trahair, N. S. (1977). The behaviour and design of steel structures. Chapman and Hall, London, U.K.
35.
Trahair, N. S. (1982). Discussion of “Wagner hypothesis in beam and column theory,” by Morris Ojalvo, J. Engrg. Mech. Div., ASCE, 108(3), 575–578.
36.
Trahair, N. S., and Papangelis, J. P. (1986). “Flexural‐torsional buckling of monosymmetric arches.” Research Report R534, School of Civ. and Mining Engrg., Univ. of Sydney, Sydney, Australia.
37.
Vacharajittiphan, P., and Trahair, N. S. (1974). “Warping and distortion at I‐section joints.” J. Struct. Div., ASCE, 100(3), 547–564.
38.
Vacharajittiphan, P., and Trahair, N. S. (1975). “Flexural‐torsional buckling of curved members.” J. Struct. Div., ASCE, 101(6), 1223–1238.
39.
Vlasov, V. Z. (1961). Thin‐walled elastic beams. 2nd ed., Israel Program for Scientific Translation, Jerusalem, Israel.
40.
Wang, C. M., and Kitipornchai, S. (1985). “Buckling of capacities of monosymmetric I‐beams.” Research Report CE62, Dept. of Civ. Engrg., Univ. of Queensland, Brisbane, Australia.
41.
Wang, C. M., and Kitipornchai, S. (1986). “Stability of monosymmetric cantilevers.” Engrg. Structures, 8(3), 169–180.
42.
Wen, R. K., and Lange, J. (1981). “Curved beam element for arch buckling analysis.” J. Struct. Div., ASCE, 107(11), 2053–2069.
43.
Winter, G. (1941). “Lateral stability of unsymmetrical I‐beams and trusses in bending.” Proc., ASCE, 67(10), 1851–1864.
44.
Yang, Y. B., and Kuo, S. R. (1986). “Static stability of curved thin‐walled beams.” J. Engrg. Mech., ASCE, 112(8), 821–841.
45.
Yoo, C. H. (1982). “Flexural‐torsional stability of curved beams.” J. Engrg. Mech. Div., ASCE, 108(6), 1351–1369.
46.
Yoo, C. H., and Pfeiffer, P. A. (1983). “Elastic stability of curved members.” J. Struct. Engrg., ASCE, 109(12), 2922–2940.
47.
Yoo, C. H., and Pfeiffer, P. A. (1984). “Buckling of curved beams with in‐plane deformation.” J. Struct. Engrg., ASCE, 110(2), 291–300.
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Copyright © 1987 ASCE.
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Published online: Oct 1, 1987
Published in print: Oct 1987
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