Effect of Axial Loads on Radial Stress in Curved Beams
Keywords:Axial loads, beams, radial stress
Radial tension failures have occurred in some curved glulam beams. Radial stresses in curved beams are generally computed using only the bending moment, e.g., Wilson's equation. This work was performed to provide additional insight into the effect on the radial stresses due to the axial loads that are present in the curved beams.
Equations of tangential, radial, and shear stress were developed for curved beams under an axial load. The theory of elasticity with polar coordinates for plane stress applied to an orthotropic material was used. Two loblolly pine glulam specimens (orthotropic) and one aluminum specimen (isotropic) with sharp radii and high d/R ratios were tested for the purpose of verifying the theoretical tangential and radial stress distributions that were predicted by the equations. In the aluminum specimen test, theoretical and experimental values compare favorably. In the glulam specimem tests, a favorable agreement was obtained for the tangential stress between the theoretical and experimental values, while the experimental radial stress values were about 2 to 4 times larger than the theoretical values.
The theoretical radial stresses predicted by Wilson's equation were verified by a rigorous theory of elasticity solution as both solutions gave almost identical results. Since the elasticity solution included the effect of axial load, we conclude that the effect of axial load on the radial stress in curved beams is small.
American Institute of Timber Construction. 1966. Timber construction manual. 1st ed., John Wiley and Sons, N.Y.nAmerican Society of Civil Engineers. 1975. A design guide and commentary—Wood structures.nFoschi. R. O. 1968. Plane-stress problem in a body with cylindrical anisotropy with special reference to curved Douglas-fir beams. Dep. Publ. No. 1244, Dep. Forest Rural Development, Ottawa, Ontario.nFox, S. P. 1970. Experimental verification of a stress analysis method for the double-tapered pitched glued-laminated beam. Dep. Publ. No. 1277, Department of Fisheries and Forestry, Canadian Forest Service. Vancouver, B.C., Canada.nNorris. C. B. 1963. Stress within curved laminated beams of Douglas-fir. FPL-20, Forest Prod. Lab., Madison. WI.nOden, T. J. 1967. Mechanics of elastic structures. McGraw-Hill, N.Y.nTimoshenko, S., and J. N. Goodier. 1951. Theory of elasticity. 2nd ed., McGraw-Hill, N.Y. Pp. 83-88.nWilson, T. R. C. 1939. The glued-laminated wooden arch. Technical Bulletin No. 691, USDA. Washington D.C. Pp. 118-119.nZahn, John J. 1969. Residual stress in curved laminated beam. J. of Structures Div., Proc. of the American Society of Civil Engineers, 95 (ST 12). Pp. 2873-2890.n
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