Warping Solution for Shear Lag in Thin-Walled Orthotropic Composite Beams
Publication: Journal of Engineering Mechanics
Volume 122, Issue 5
Abstract
A warping solution for prismatic thin-walled orthotropic composite beams is presented. For beam-wall macroelements, the macro approach solution is applied to obtain the displacements as a sum of polynomial plus Fourier functions. The kinematics of a beam-wall are obtained from a generalized plane stress solution. Constitutive equations that account for both slender and stiffened FRP sections are proposed. A fast converging continuous closed-form solution is obtained for the macroelement. The wall displacement field is evaluated in terms of nodal line parameters. Elastic coefficients that account for warping effects are introduced to provide a mechanics interpretation of the formulation. The macroelement assembling technique is illustrated by presenting an explicit warping solution for bending of box beams. The warping solution is correlated with existing analytical solutions. An expression for both the effective width and the effective longitudinal modulus variation in flanges of box beams is presented. A design equation consistent with current practice is proposed.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barbero, E. J., and GangaRao, H. V. S.(1991). “Structural applications of composites in infrastructure, (Part 1).”SAMPE J., 27(6), 9–16.
2.
Barbero, E. J., and GangaRao, H. V. S.(1992). “Structural applications of composites in infrastructure, (Part 2).”SAMPE J., 28(1), 9–16.
3.
Barbero, E. J., Lopez-Anido, R., and Davalos, J. F.(1993). “On the mechanics of thin-walled laminated composite beams.”J. Composite Mat., 27(8), 806–829.
4.
Bauchau, O. A.(1985). “A beam theory for anisotropic materials.”J. Appl. Mech., 52, 416–422.
5.
Bauld, N. R., and Tzeng, L. S.(1984). “A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections.”Int. J. Solids Struct., 20(3), 277–297.
6.
Burgan, B. A., and Dowling, P. J.(1990). “The treatment of shear lag in design.”Thin-Walled Struct., 9, 121–134.
7.
Chandra, R., and Chopra, I.(1991). “Experimental and theoretical analysis of composite I-beams with elastic coupling.”AIAA J., 29(12), 2197–2206.
8.
Gjelsvik, A. (1981). The theory of thin-walled bars. John Wiley and Sons, New York, N.Y.
9.
Hjelmstad, K. D.(1987). “Warping effects in transverse bending of thin-walled beams.”J. Engrg. Mech., ASCE, 113(6), 907–924.
10.
Horgan, C. O.(1972). “Some remarks on Saint-Venant's principle for transversely isotropic composites.”J. Elasticity, 2(4), 335.
11.
Jolley, L. B. W. (1961). Summation of series . Dover Publications, New York, N.Y.
12.
Jones, R. (1975). Mechanics of composite materials . Hemisphere, New York, N.Y.
13.
Koo, K. K., and Cheung, Y. K.(1989). “Mixed variational formulation for thin-walled beams with shear lag.”J. Engrg. Mech., ASCE, 115(10), 2271–2286.
14.
Laudiero, F., and Savoia, M.(1990). “Shear strain effects in flexure and torsion of thin-walled beams with open or closed cross-section.”Thin-Walled Struct., 10, 87–119.
15.
Lekhnitskii, S. G. (1968). Anisotropic plates . Gordon and Breach, New York, N.Y.
16.
Librescu, L., and Song, O. (1991). “Behavior of thin-walled beams made of advanced composite materials and incorporating non-classical effects.”Appl. Mech. Rev., 44(11), Part 2, S174–S180.
17.
Lopez-Anido, R. (1995). “Analysis and design of orthotropic plates stiffened by laminated beams for bridge superstructures,” dissertation. West Virginia Univ., Morgantown, W.Va.
18.
Lopez-Anido, R., Davalos, J. F., and Barbero, E. J.(1995). “Experimental evaluation of stiffness of laminated composite beam elements under flexure.”J. Reinforced Plastics and Comp., 14(4), 349–361.
19.
Love, A. E. H. (1952). A treatise on the mathematical theory of elasticity . Cambridge University Press, Cambridge, U.K.
20.
Massonnet, C. E.(1983). “A new approach (including shear lag) to elementary mechanics of materials.”Int. J. Solids Struct., 19(1), 33–54.
21.
Nagaraj, V., and GangaRao, H. V. S. (1993). “Characterization of GFRP pultruded box beams under static and fatigue loads.”SAMPE Q., 3–9.
22.
Nagaraj, V., and GangaRao, H. V. S. (1994). “Static and fatigue response of pultruded FRP beams without and with splice connection.”CFC Rep. No. CFC-94-194, Constr. Fac. Ctr., West Virginia Univ., Morgantown, W.Va.
23.
Peshkam, V., and Dawe, D.(1989). “Buckling and vibration of finite-length composite prismatic plate structures with diaphragm ends, part ii: Computer program and buckling applications.”Comp. Methods in Appl. Mech. and Engrg., 77, 227–252.
24.
Rehfield, L. W., Hodges, D. H., and Atilgan, A. R. (1988). “Some considerations on the nonclassical behavior of thin-walled composite beams.”Nat. Tech. Specialists' Meeting on Adv. Rotorcraft Struct., AHS, Williamsburg, Va.
25.
Reissner, E. (1941). Least work solutions of shear lag problems. J. Aeronautical Sci., 8(7), 284–291.
26.
Reissner, E.(1946). “Analysis of shear lag in box beams by the principle of minimum potential energy.”Q. Appl. Math., 6(3), 268–278.
27.
Skudra, A. M., Bulavs, F. Y., Gurvich, M. R., and Kruklinsh, A. A. (1991). Structural analysis of composite beams . Technomic, Lancaster, Pa.
28.
Song, Q., and Scordelis, A. C.(1990a). “Formulas for shear-lag effect of T-, Iand box beams.”J. Struct. Engrg., ASCE, 116(5), 1306–1318.
29.
Song, Q, and Scordelis, A. C.(1990b). “Shear-lag analysis of T-, Iand Box beams.”J. Struct. Engrg., ASCE, 116(5), 1290–1305.
30.
Sotiropoulos, S., GangaRao, H. V. S., and Mongi, A. N. K.(1994). “Theoretical and experimental evaluation of FRP components and systems.”J. Struct. Engrg., ASCE, 120(2), 464–485.
31.
Szilard, R. (1974). Theory and analysis of plates . Prentice-Hall, Englewood Cliffs, N.J.
32.
Takayanagi, H., Kemmochi, K., Sembokuya, H., Hojo, M., and Maki, H.(1994). “Shear-lag effect in CFRP I-beams under three-point bending.”Experimental Mech., 34(2), 100–107.
33.
Tripathy, A. K., Patel, H. J., and Pang, S. S.(1994). “Bending analysis of laminated composite box beams.”J. Engrg. Mat. and Technol., 116, 121–129.
34.
Tsai, S. W. (1988). Composites design . Think Composites, Dayton, Ohio.
35.
Wekezer, J. W.(1986). “Free vibrations of thin-walled bars with open cross sections.”J. Engrg. Mech., ASCE, 113(10), 1441–1452.
36.
Wu, X. X., and Sun, C. T.(1990). “Vibration analysis of laminated composite thin-walled beams using finite elements.”AIAA J., 29(5), 736–742.
37.
Wu, X. X., and Sun, C. T.(1992). “Simplified theory for composite thin-walled beams.”AIAA J., 30(12), 2945–2951.
Information & Authors
Information
Published In
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jan 19, 1996
Published in print: May 1, 1996
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.