Exact Stiffness Matrix for Nonprismatic Beams with Parabolic Varying Depth
Main Article Content
Abstract
In this paper, an exact stiffness matrix and fixed-end load vector for nonprismatic beams having parabolic varying depth are derived. The principle of strain energy is used in the derivation of the stiffness matrix.
The effect of both shear deformation and the coupling between axial force and the bending moment are considered in the derivation of stiffness matrix. The fixed-end load vector for elements under uniformly distributed or concentrated loads is also derived. The correctness of the derived matrices is verified by numerical examples. It is found that the coupling effect between axial force and bending moment is significant for elements having axial end restraint. It was found that the decrease in bending moment was
in the range of 31.72%-42.29% in case of including the effect of axial force for the studied case. For midspan deflection, the decrease was 46.07% due to the effect of axial force generated at supports as a result of axial restraint.
Article Details
Section
How to Cite
References
Al-Gahtani, H. J. (1996). "Exact stiffnesses for tapered members" J. Struct. Eng., 122(10), 1234-1239.
Al-Gahtani, H. J., and Khan, M. S. (1998). "Exact analysis of nonprismatic beams" J. Eng. Mech., 124(11), 1290-1293.
Bathe, K. J., (1996). "Finite element procedures" Prentice-Hall, New Jersey.
Boresi, A. P., and Schmidt, R. J. (2003). "Advanced mechanics of materials" 6th Ed., Wiley, New York.
Khan, M. S., and Al-Gahtani, H. J. (1995). "Analysis of continuous non-prismatic beams using boundary procedures" The Fourth Saudi
Engineering Conference, V11, 137-145.
Luo, Y., Xu, X., and Wu, F. (2007). "Accurate stiffness matrix for nonprismatic members" J. Struct. Eng., 133(8), 1168-1175.
Timoshenko, S. P., and Young, D. H. (1965). "Theory of structures" 2nd Ed., McGraw-Hill, New York.