| A simple analytical method for analyzing fiber reinforced polymeric composite beams with hat cross-section is presented. The method includes development of closed-form expression of the axial, bending and their coupling stiffness matrices for the composite beams. The stiffness matrices are obtained by transforming the actual geometrical cross-section of the beam into an equivalent plate using transformation matrices and Parallel Axis theorem. Ply stresses due to mechanical as well as thermal load can easily be obtained at any given location of the beam section. In this approach, the effect of induced in-plane deformation due to bending for an unsymmetrical cross-section is included while the conventional analysis, using the smeared properties, ignores this coupling effect. Finite element analysis was conducted to obtain the results for comparison. It is concluded that the axial and bending stiffness obtained by the present method gives excellent agreement to the finite element results as compared with the conventional method. Significant error is observed for axial stiffness comparison between conventional and finite element results. Experimental bending stiffness values of I-beams are also used for comparison and good conformity is observed using present method.; A simple closed form solution is derived based on the extensional application of developed method to obtain ply stresses due to thermal loading. Results were validated and excellent agreement is observed with the finite element model.; Location of centroid and shear center plays an important role in engineering analysis as extension/bending and bending/twisting are decoupled at these locations, respectively. For composite material, these locations are dependent not only on cross sectional geometry but also on the material properties. Based on the stiffness matrices obtained, a simple methodology is developed to determine these locations. Results are validated by comparing with isotropic materials and also by observing the behavior of composite material for symmetric and unsymmetric cases. It is concluded that the present method provides generic solution for the design and analysis of laminated composite beams with significant accuracy and ease. The developed tool is handy in providing the parametric study for composite structural design. |
